how to solve a synthetic division problem

Practice Problem 1a: Divide using synthetic division.

Practice Problem 2a: Given the function f ( x ), use the Remainder Theorem to find f (-1).

Practice Problem 3a: Solve the given equation given that 1/2 is a zero (or root) of .

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Synthetic Division

In these lessons, we will look at Synthetic Division, which is simplified form of long division.

What is Synthetic Division?

Synthetic Division is an abbreviated way of dividing a polynomial by a binomial of the form ( x + c ) or ( x – c ). We can simplify the division by detaching the coefficients.

Example: Evaluate ( x 3 – 8 x + 3) ÷ ( x + 3) using synthetic division

Solution: ( x 3 – 8 x + 3) is called the dividend and ( x + 3) is called the divisor.

Step 1: Write down the constant of the divisor with the sign changed –3

Step 2: Write down the coefficients of the dividend. (Remember to add a coefficient of 0 for the missing terms)

how to solve a synthetic division problem

Step 3: Bring down the first coefficient.

Step 4: Multiply (1)( –3) = –3 and add to the next coefficient.

Repeat Step 4 for all the coefficients

We find that ( x 3 – 8 x + 3) ÷ ( x + 3) = x 2 – 3 x + 1

It is easier to learn Synthetic Division visually. Please watch the following videos for more examples of Synthetic Division.

Polynomial Division: Synthetic Division Perform synthetic division to divide by a binomial in the form (x - k)

Example: Divide using synthetic division

(2x 3 + 6x 2 + 29) ÷ (x + 3)

(2x 3 + 6x 2 - 17x + 15) ÷ (x + 5)

(y 5 - 32) ÷ (y - 2)

(16x 3 - 2 + 14x - 12x 2 ) ÷ (2x + 1)

Divide a Trinomial by a Binomial Using Synthetic Division

(x 2 - 5x + 7) ÷ (x - 2)

(x 2 + 8x + 12) ÷ (x + 2)

Synthetic Division This video shows how you can use synthetic division to divide a polynomial by a linear expression. It also shows how synthetic division can be used to evaluate polynomials.

Example: (x 3 - 2x 2 + 3x - 4) ÷ (x - 2)

Synthetic Division This video shows how to use synthetic division to divide a polynomial by a linear expression and also how to use the remainder to evaluate the polynomial.

Example: (x 4 - x 2 + 5) ÷ (x + 3)

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Module 9: Power and Polynomial Functions

Synthetic division, learning outcomes.

Use synthetic division to divide polynomials.

As we’ve seen, long division with polynomials can involve many steps and be quite cumbersome. Synthetic division is a shorthand method of dividing polynomials for the special case of dividing by a linear factor whose leading coefficient is 1.

To illustrate the process, recall the example at the beginning of the section.

Divide [latex]2{x}^{3}-3{x}^{2}+4x+5[/latex] by [latex]x+2[/latex] using the long division algorithm.

The final form of the process looked like this:

$Long division of [latex]2{x}^{3}-3{x}^{2}+4x+5[/latex] by [latex]x+2[/latex]$

There is a lot of repetition in the table. If we don’t write the variables but instead line up their coefficients in columns under the division sign and also eliminate the partial products, we already have a simpler version of the entire problem.

Synthetic division of the polynomial 2x^3-3x^2+4x+5 by x+2 in which it only contains the coefficients of each polynomial.

Synthetic division carries this simplification even a few more steps. Collapse the table by moving each of the rows up to fill any vacant spots. Also, instead of dividing by 2, as we would in division of whole numbers, and then multiplying and subtracting the middle product, we change the sign of the “divisor” to –2, multiply, and add. The process starts by bringing down the leading coefficient.

We then multiply it by the “divisor” and add, repeating this process column by column until there are no entries left. The bottom row represents the coefficients of the quotient; the last entry of the bottom row is the remainder. In this case, the quotient is [latex]2x{^2} -7x+18[/latex] and the remainder is –31. The process will be made more clear in the examples that follow.

A General Note: Synthetic Division

Synthetic division is a shortcut that can be used when the divisor is a binomial in the form x – k . In synthetic division , only the coefficients are used in the division process.

How To: Given two polynomials, use synthetic division to divide

Example: Using Synthetic Division to Divide a Second-Degree Polynomial

Use synthetic division to divide [latex]5{x}^{2}-3x - 36[/latex] by [latex]x - 3[/latex].

Begin by setting up the synthetic division. Write k and the coefficients.

A collapsed version of the previous synthetic division.

Bring down the leading coefficient. Multiply the leading coefficient by k .

$The set-up of the synthetic division for the polynomial 5x^2-3x-36 by x-3, which renders {5, -3, -36} by 3.$

Continue by adding the numbers in the second column. Multiply the resulting number by k . Write the result in the next column. Then add the numbers in the third column.

Multiplied by the lead coefficient, 5, in the second column, and the lead coefficient is brought down to the second row.

The result is [latex]5x+12[/latex]. The remainder is 0. So [latex]x - 3[/latex] is a factor of the original polynomial.

Analysis of the Solution

Just as with long division, we can check our work by multiplying the quotient by the divisor and adding the remainder.

[latex]\left(x - 3\right)\left(5x+12\right)+0=5{x}^{2}-3x - 36[/latex]

Example: Using Synthetic Division to Divide a Third-Degree Polynomial

Use synthetic division to divide [latex]4{x}^{3}+10{x}^{2}-6x - 20[/latex] by [latex]x+2[/latex].

Synthetic division of 4x^3+10x^2-6x-20 divided by x+2.

The result is [latex]4{x}^{2}+2x - 10[/latex]. The remainder is 0. Thus, [latex]x+2[/latex] is a factor of [latex]4{x}^{3}+10{x}^{2}-6x - 20[/latex].

The graph of the polynomial function [latex]f\left(x\right)=4{x}^{3}+10{x}^{2}-6x - 20[/latex] shows a zero at [latex]x=-2[/latex]. This confirms that [latex]x+2[/latex] is a factor of [latex]4{x}^{3}+10{x}^{2}-6x - 20[/latex].

Example: Using Synthetic Division to Divide a Fourth-Degree Polynomial

Use synthetic division to divide [latex]-9{x}^{4}+10{x}^{3}+7{x}^{2}-6[/latex] by [latex]x - 1[/latex].

The result is [latex]-9{x}^{3}+{x}^{2}+8x+8+\frac{2}{x - 1}[/latex].

Use synthetic division to divide [latex]3{x}^{4}+18{x}^{3}-3x+40[/latex] by [latex]x+7[/latex].

[latex]3{x}^{3}-3{x}^{2}+21x - 150+\frac{1,090}{x+7}[/latex]

https://www.myopenmath.com/multiembedq.php?id=29483&theme=oea&iframe_resize_id=mom1

Polynomial division can be used to solve a variety of application problems involving expressions for area and volume. We looked at an application at the beginning of this section. Now we will solve that problem in the following example.

Example: Using Polynomial Division in an Application Problem

The volume of a rectangular solid is given by the polynomial [latex]3{x}^{4}-3{x}^{3}-33{x}^{2}+54x[/latex]. The length of the solid is given by 3 x and the width is given by x – 2. Find the height of the solid.

There are a few ways to approach this problem. We need to divide the expression for the volume of the solid by the expressions for the length and width. Let us create a sketch.

Graph of f(x)=4x^3+10x^2-6x-20 with a close up on x+2.

We can now write an equation by substituting the known values into the formula for the volume of a rectangular solid.

[latex]\begin{array}{l}V=l\cdot w\cdot h\\ 3{x}^{4}-3{x}^{3}-33{x}^{2}+54x=3x\cdot \left(x - 2\right)\cdot h\end{array}[/latex]

To solve for h , first divide both sides by 3 x .

[latex]\begin{array}{l}\frac{3x\cdot \left(x - 2\right)\cdot h}{3x}=\frac{3{x}^{4}-3{x}^{3}-33{x}^{2}+54x}{3x}\\ \left(x - 2\right)h={x}^{3}-{x}^{2}-11x+18\end{array}[/latex]

Now solve for h using synthetic division.

[latex]h=\frac{{x}^{3}-{x}^{2}-11x+18}{x - 2}[/latex]

Synthetic division with 2 as the divisor and {1, -1, -11, 18} as the quotient. The result is {1, 1, -9, 0}

The quotient is [latex]{x}^{2}+x - 9[/latex] and the remainder is 0. The height of the solid is [latex]{x}^{2}+x - 9[/latex].

The area of a rectangle is given by [latex]3{x}^{3}+14{x}^{2}-23x+6[/latex]. The width of the rectangle is given by x + 6. Find an expression for the length of the rectangle.

[latex]3{x}^{2}-4x+1[/latex]

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Synthetic Division Method

I must say that synthetic division is the most “fun” way of dividing polynomials. It has fewer steps to arrive at the answer as compared to the polynomial long division method . In this lesson, I will go over five (5) examples that should hopefully make you familiar with the basic procedures in successfully dividing polynomials using synthetic division.

Things to Remember:

Examples of How to Divide Polynomials Using the Synthetic Division

Example 1 : Divide the polynomial below.

Let us re-examine the given problem and make the necessary adjustments, if necessary.

The dividend (stuff to divide) is in standard form because the exponents are in decreasing order. That’s good!

The divisor needs to be rewritten as

At this point, I can now set up the synthetic division by extracting the coefficients of the dividend and then lining them up on top.

Directly to the left side, place the value of c = - 2 inside the “box”.

Finally, construct a horizontal line just below the coefficients of the dividend.

1. Drop the first coefficient below the horizontal line.

2. Multiply that number you drop by the number in the “box”. Whatever its product, place it above the horizontal line just below the second coefficient.

3. Add the column of numbers, then put the sum directly below the horizontal line.

4. Repeat the process until you run out of columns to add.

See the animated solution below:

The last number below the horizontal line is always the remainder! The remainder of this problem is 3 .

So how do we present our final answer?

Show your final answer in the form

Notice that the numbers below the horizontal line except the last (remainder) are the coefficients of the Quotient.

More so, the exponents of the variables of the quotient are all reduced by 1 .

Example 2 : Divide the polynomial.

This is not a trick question. Notice that the quotient does not have all the exponents of the variable x .

I can see that we are missing {x^4} and {x^2} . To include all the coefficients of variable x in decreasing power, we should rewrite the original problem like this. Attach zeroes on those missing x ‘s. Also express the divisor as x - (c) which clearly reveals the value of c , that is, c = + 1 .

From this point, I can now set up the numbers to continue with the process.

See animated solution below:

So putting the final answer in the form

we have

Example 3 : Divide the polynomial below.

\left( { - 2{x^4} + x} \right) \div \left( {x - 3} \right)

This is becoming more interesting! The quotient definitely looks horrible because it is missing a lot. Not only it lacks some x ‘s which are {x^3} and {x^2} but the constant is also gone.

To fix this, I will rewrite the original problem in such a way that all x ‘s are accounted for. But more importantly, do not forget to include the missing constant which is zero.

The “new and improved” problem should look like this:

From here, proceed with the steps as usual.

Okay then, the final answer for this is

You can write the final answer in two ways. The first one is using the minus or subtraction symbol to indicate that the remainder is negative. The second one is using the + symbol but attaching a negative symbol to the numerator. They mean the same thing!

Example 4 : Divide the polynomial below.

\left( { - {x^5} + 1} \right) \div \left( {x + 1} \right)

Don’t be discouraged by this problem. This is actually quite easy especially now that you have gone through a few examples already. Always remember to “fill in the missing parts”, right?

Observe the dividend and you should agree that the missing parts are {x^4} , {x^3} , {x^2} , and x .

Rewriting the original problem that is synthetic-division ready, we get…

We populated the missing x ‘s with zeros and explicitly solve for c = -1 .

The last number below the horizontal line will always be the remainder. Don’t forget that. In this case, the remainder equals 2 .

Our final answer is

Example 5 : Divide the polynomial by a binomial.

In this example, we will get a remainder of zero. When that happens the divisor becomes a factor of the dividend. In other words, the divisor evenly divides the dividend.

By examining the problem, I see that there are no missing components. All powers of x ‘s are accounted for, and we have a constant. That’s great! This problem is in fact synthetic-division ready.

Because the remainder equals zero, this means the divisor x - 5 is a factor of the dividend

How to Divide Polynomials Using Synthetic Division

Last Updated: May 23, 2021 References

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Synthetic division is a shorthand method of dividing polynomials where you divide the coefficients of the polynomials, removing the variables and exponents. It allows you to add throughout the process instead of subtract, as you would do in traditional long division. [1] X Research source If you want to know how to divide polynomials using synthetic division, just follow these steps.

Image titled Divide Polynomials Using Synthetic Division Step 1

-2 | 1 2 -4 8 ↓ 1

Image titled Divide Polynomials Using Synthetic Division Step 6

-2 | 1 2 -4 8 -2 1

Image titled Divide Polynomials Using Synthetic Division Step 7

-2 | 1 2 -4 8 -2 1 0

Image titled Divide Polynomials Using Synthetic Division Step 8

-2 | 1 2 -4 8 -2 0 1

Image titled Divide Polynomials Using Synthetic Division Step 9

-2 | 1 2 -4 8 -2 0 1 0 -4

Image titled Divide Polynomials Using Synthetic Division Step 10

-2 | 1 2 -4 8 -2 0 8 1 0 -4 | 16

Image titled Divide Polynomials Using Synthetic Division Step 11

-2 | 1 2 -4 8 -2 0 8 1 0 -4 | 16 x 2 + 0 x - 4 R 16 x 2 - 4 R16

Image titled Divide Polynomials Using Synthetic Division Step 12

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To check your answer, multiply the quotient by the divisor and add the remainder. It should be the same as the original polynomial. [4] X Research source (divisor)(quotient)+(remainder) ( x + 2)( x 2 - 4) + 16 Using FOIL method, multiply. ( x 3 - 4 x + 2 x 2 - 8) + 16 x 3 + 2 x 2 - 4 x - 8 + 16 x 3 + 2 x 2 - 4 x + 8 ⧼thumbs_response⧽ Helpful 2 Not Helpful 1

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Synthetic Division: The Process

The Process Worked Examples Finding Zeroes Factoring Polynomials

What is synthetic division?

Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor — and it only works in this case. Synthetic division is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials. More about this later.

Content Continues Below

MathHelp.com

How are polynomial zeroes and factors related?

If you are given, say, the polynomial equation y = x 2 + 5x + 6 , you can factor the polynomial as y = ( x + 3)( x + 2) . Then you can find the zeroes of y by setting each factor equal to zero and solving. You will find that the two zeroes of the polynomial are x = −2 and x = −3 .

You can, however, also work backwards from the zeroes to find the originating polynomial. For instance, if you are given that x = −2 and x = −3 are the zeroes of a quadratic, then you know that x + 2 = 0 , so x + 2 is a factor, and x + 3 = 0 , so x + 3 is a factor. Therefore, you know that the quadratic must be of the form y = a ( x + 3)( x + 2) .

(The extra number " a " in that last sentence is in there because, when you are working backwards from the zeroes, you don't know toward which quadratic you're working. For any non-zero value of " a ", your quadratic will still have the same zeroes. But the issue of the value of " a " is just a technical consideration; as long as you see the relationship between the zeroes and the factors, that's all you really need to know for this lesson.)

Anyway, the above is a long-winded way of saying that, if x − n is a factor, then x = n is a zero, and if x = n is a zero, then x − n is a factor. And this is the fact you use when you do synthetic division.

Let's look again at the quadratic from above: y = x 2 + 5 x + 6 . From the Rational Roots Test , we know that ± 1, 2, 3, and 6 are possible zeroes of the quadratic. (And, from the factoring above, we know that the zeroes are, in fact, −3 and −2 .) How would you use synthetic division to check the potential zeroes?

Well, think about how long polynomial divison works. If I were to guess that x = 1 is a zero, then this means that x − 1 is a factor of the quadratic. And if it's a factor, then it will divide out evenly; that is, if we divide x 2 + 5 x + 6 by x − 1 , we would get a zero remainder. Let's check:

As expected (since we know that x − 1 is not a factor), we got a non-zero remainder. What does this look like in synthetic division?

How do you do synthetic division?

First, take the polynomial (in our case, x 2 + 5 x + 6 ), and write the coefficients ONLY inside an upside-down division-type symbol:

Make sure you leave room inside, underneath the row of coefficients, to write another row of numbers later.

Put the test zero, in our case x = 1 , at the left, next to the (top) row of numbers:

Take the first number that's on the inside, the number that represents the polynomial's leading coefficient, and carry it down, unchanged, to below the division symbol:

Multiply this carry-down value by the test zero on the left, and carry the result up into the next column inside:

Add down the column:

Multiply the previous carry-down value by the test zero, and carry the new result up into the last column:

This last carry-down value is the remainder.

Comparing, you can see that we got the same result from the synthetic division, the same quotient (namely, 1 x + 6 ) and the same remainder at the end (namely, 12 ), as when we did the long division:

The results are formatted differently, but you should recognize that each format provided us with the same result, being a quotient of x + 6 , and a remainder of 12 .

We already know (from the factoring above) that x + 3 is a factor of the polynomial, and therefore that x = −3 is a zero.

Now let's compare the results of long division and synthetic division when we use the factor x + 3 (for the long division) and the zero x = −3 (for the synthetic division):

As you can see above, while the results are formatted differently, the results are otherwise the same:

In the long division, I divided by the factor x + 3 , and arrived at the result of x + 2 with a remainder of zero. This means that x + 3 is a factor, and that x + 2 is left after factoring out the x + 3 . Setting the factors equal to zero, I get that x = −3 and x = −2 are the zeroes of the quadratic.

In the synthetic division, I divided by x = −3 , and arrived at the same result of x + 2 with a remainder of zero. Because the remainder is zero, this means that x + 3 is a factor and x = −3 is a zero. Also, because of the zero remainder, x + 2 is the remaining factor after division. Setting this equal to zero, I get that x = −2 is the other zero of the quadratic.

I will return to this relationship between factors and zeroes throughout what follows; the two topics are inextricably intertwined.

URL: https://www.purplemath.com/modules/synthdiv.htm

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Synthetic Division

In algebra, the synthetic division is one of the methods used to manually perform the Euclidean division of polynomials. The division of polynomials can also be done using the long division method. But, in comparison to the long division method of polynomials, the synthetic division requires lesser writing and fewer calculations. That means the synthetic division is the shorter method of the traditional long-division of a polynomial for the special cases when dividing by a linear factor.

Let us understand the method to perform the synthetic division of polynomials in detail using solved examples.

What is Synthetic Division?

Synthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor. One of the advantages of using this method over the traditional long method is that the synthetic division allows one to calculate without writing variables while performing the polynomial division , which also makes it an easier method in comparison to the long division .

We can represent the division of two polynomials in the form: p(x)/q(x) = Q(x) + R/(q(x))

Synthetic Division of Polynomials Definition

When we divide a polynomial p(x) by a linear factor (x - a) (which is a polynomial of degree 1), Q(x) is the quotient polynomial and R is the remainder .

p(x)/q(x) = p(x)/(x- a) = Quotient + (Remainder/(x - a))

p(x)/(x - a) = Q(x) + (R/(x - a))

The coefficients of p(x) are taken and divided by the zero of the linear factor.

We use synthetic division in the context of the evaluation of the polynomials by the remainder theorem, wherein we evaluate the value of p(x) at "a" while dividing (p(x)/(x - a)). That is, to find if "a" is the factor of the polynomial p(x), use the synthetic division to find the remainder quickly. Let us understand this better using the example given below.

Synthetic Division Example

Richard sells apples. The previous day, his profits were x, and today, his profits are ((x × x) - 2). If the number of apples he sold was (x + 2), what was the profit made per apple? We obtain the solution by modelling the equation as (x 2 + x - 2) ÷ (x + 2).

Step 1: Write the coefficients of the dividend inside the box and zero of x + 2 as the divisor.

Step 2: Bring down the leading coefficient 1 to the bottom row.

Step 3: Multiply -2 by 1 and write the product -2 in the middle row.

Step 4: Add 1 and -2 in the second column and write the sum -1 in the bottom row.

Step 5: Now, multiply -2 by -1 (obtained in step 4) and write product 2 below -2.

Step 6: Add -2 and 2 in the third column and write the sum 0 in the bottom row.

Step 7: The bottom row gives the coefficient of the quotient. The degree of the quotient is one less than that of the dividend. So, the final answer is x - 1 + 0/(x + 2) = x - 1.

Please note that the last box in the bottom row gives the remainder.

Synthetic division of polynomials example

The profit per apple is given by (x - 1).

Synthetic Division vs Long Division

Let us see how long division differs from the synthetic division of polynomials by comparing both methods. In the example given below, we will perform the division of the polynomial 4x 2 - 5x - 21 by a linear polynomial x - 3.

In the example given below, another polynomial 2x 2 + 3x - 1 is divided by a linear polynomial x + 1. When a polynomial P(x) is to be divided by a linear factor, we write the coefficients alone, bring down the first coefficient, multiply, and add. Repeat the multiplication and addition until we reach the end term of the polynomial.

Using synthetic division, we can perform complex division and obtain the solutions easily.

Synthetic Division Method

The following are the steps while performing synthetic division and finding the quotient and the remainder. We will take the following expression as a reference to understand it better: (2x 3 - 3x 2 + 4x + 5)/(x + 2)

Repeat the previous 2 steps until you reach the last term.

Therefore, the result obtained after synthetic division of (2x 3 - 3x 2 + 4x + 5)/(x + 2) is 2x 2 - 7x + 18 and remainder is -31

How to do Synthetic Division?

Synthetic division of polynomials uses numbers for calculation and avoids the usage of variables . In the place of division, we multiply, and in the place of subtraction, we add.

1) Consider this division: (x 3 - 2x 3 - 8x - 35)/(x - 5). The polynomial is of order 3. The divisor is a linear factor. Let's use synthetic division to find the quotient. Thus, the quotient is one order less than the given polynomial. It is x 2 + 3x + 7 and the remainder is 0. (x 3 - 2x 3 - 8x - 35)/(x - 5) = x 2 + 3x + 7.

Tips and Tricks on Synthetic Division:

☛ Related Articles:

Synthetic Division Examples

Example 1: The distance covered by Steve in his car is given by the expression 9a 2 - 39a - 30. The time taken by him to cover this distance is given by the expression (a - 5). Find the speed of the car.

Speed is given as the ratio of the distance to the time.

Speed = (9a 2 - 39a - 30)/(a - 5)

Speed = (9a + 6)

Answer: Speed is given by the expression 9a + 6.

Example 2: The volume of Sara's storage box is 8x 3 + 12x 2 - 2x - 3. She knows that the area of the box is 4x 2 - 1. What could be the height of the box?

Area (A) = length(l) × breadth(b)

Given A = 4x 2 - 1. This is of the form a 2 - b 2 = (a + b)(a - b)

This can be expressed as, A = (2x + 1)(2x - 1)

V = l × b × h = A × h

h = (V/A) = (8x 3 + 12x 2 - 2x - 3)/[(2x + 1)(2x - 1)]

Let's solve this by the synthetic division twice.

Answer: Height of the box = 2x + 3.

Example 3: Perform synthetic division to solve the following expression: (6x 2 + 7x - 20)/(2x + 5).

Let us have a look at the steps shown below,

Answer: Quotient for the given division of polynomials = 3x - 4.

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Practice Questions on Synthetic Division

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FAQs on Synthetic Division

When a polynomial has to be divided by a linear factor, the synthetic division is the shortest method. It is an alternative to the traditional long division method used to solve the polynomial division.

How do you Divide Polynomials by Synthetic Division?

We can perform synthetic division using some general steps. Take the coefficients alone, bring the first down, multiply with the zero of the linear factor, and add with the next coefficient and repeat until the end.

What is the Importance of the Synthetic Division?

Synthetic division can be generalized and expanded to the division of any polynomial with any polynomial. It is an easier method in comparison to the long division method for performing division on polynomials with the linear divisor.

What are the Advantages of the Synthetic Division of Polynomials?

This method uses fewer calculations and is quicker than long division. It takes comparatively lesser space while computing the steps involved in the polynomial division.

What are the Disadvantages of Synthetic Division?

The synthetic division can be used only when the divisor is a linear polynomial. We have to follow the long division method for the other cases.

What are the Main Uses of Synthetic Division of Polynomials?

Synthetic division of polynomials helps in finding the zeros of the polynomial. It also reduces the complexity of the expression while dividing the polynomials by a linear factor.

What is the Quotient in Synthetic Division?

In synthetic division, the polynomial obtained is one power lesser than the power of the dividend polynomial. The result obtained can be arranged to form the quotient of the polynomial division.

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Examples of How to Divide Polynomials Using the Synthetic Division · 1. Drop the first coefficient below the horizontal line. · 2. Multiply that number you drop
How to Divide Polynomials Using Synthetic Division: 12 Steps
Write down the problem. For this example, you will be dividing x3 + 2x2 - 4x + 8 by x + 2. Write the first polynomial equation, the dividend, in the numerator
How does synthetic division of polynomials work?
Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor — and it only works in this
Intro to polynomial synthetic division (video)
You divide out the coefficient of x, to get a divisor of the form (x-k); you can then use synthetic division to check if (x-k) is a factor of
Dividing polynomials: synthetic division (video)
Step 1: Divide p(x) with (x - 1): (4x^3 - 8x^2 - 20x + 24) / (x - 1) = 4x^2 - 4x - 24. There's no remainder, so x = 1 is indeed a root of p(x). Step 2. Factor
Synthetic Division
Synthetic Division Examples ... Example 1: The distance covered by Steve in his car is given by the expression 9a2 - 39a - 30. The time taken by him to cover this