IXL - Divide polynomials using synthetic division (Precalculus practice)

Use synthetic division to find

(

–

)

(

)

Write your answer in the form

(

)

(

)

where

(

)

is a polynomial,

is an integer, and

(

)

is a linear polynomial. Simplify any fractions.

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Learn with an example

question

Use synthetic division to find

(

–

)

(

–

)

Write your answer in the form

(

)

(

)

where

(

)

is a polynomial,

is an integer, and

(

)

is a linear polynomial. Simplify any fractions.

key idea

Synthetic division is a way to divide a polynomial (called the dividend) by a polynomial of the form

–

(called the divisor). The result of the division is a polynomial (called the quotient) and a remainder. It is an alternative method to polynomial long division.

solution

The polynomial

–

is the dividend.

The linear factor

–

is the divisor. Since it has the form

–

follow the steps to divide by synthetic division.

Step 1: Write the root of the divisor and the coefficients of the dividend on the same line, but separated with a corner symbol.

The root of the divisor is

The coefficients of the dividend

–

are 1,

–

and 4.

–

Step 2: Bring down the first coefficient.

–

Step 3: Multiply the rightmost number on the bottom row by the root and write the product under the next coefficient. Then, add the terms in that column. Repeat this process until all columns are filled.

The rightmost number on the bottom row is 1 and the root is 2, so their product is 2. Write 2 underneath the second coefficient,

–

and add.

–

The rightmost number on the bottom row is

–

and the root is 2, so their product is

–

Write

–

underneath the next coefficient, 4, and add.

–

Step 4: Identify the quotient and remainder.

The numbers to the left of the line on the bottom row (1 and

–

)

are the coefficients of the quotient written in order of descending degree:

–

The quotient starts with an

term since the dividend starts with an

term. (The degree of the quotient is one less than the degree of the dividend because the degree of the divisor is 1.)

The number to the right of the line on the bottom row,

–

is the remainder.

Step 5: Write the result.

You know the quotient

(

)

–

the remainder

–

and the divisor

(

)

–

Now write your answer in the form

(

)

(

)

(

–

)

(

–

)

–

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E.2Divide polynomials using long division

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