IXL - Evaluate polynomials using synthetic division (Precalculus practice)

(

)

use synthetic division to find

(

–

)

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Learn with an example

question

(

)

use synthetic division to find

(

–

)

key idea

The Remainder Theorem says that if a non-constant polynomial

(

)

is divided by

(

–

)

where

is a constant, then the remainder is

(

)

(

)

is the quotient, this means:

(

)

(

)

(

–

)

(

)

According to the Remainder Theorem, synthetic division can be used to evaluate a polynomial

(

)

at a constant

Write

followed by the coefficients of

(

)

on the top line. Then, perform synthetic division. The remainder is

(

)

solution

Since you want to find

(

–

)

write the input value of

–

in a box on the left. Then write the coefficients of

(

)

on the same line and perform synthetic division.

–

Bring down the first coefficient.

–

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

–

Identify the remainder.

The remainder is 37, so

(

–

)

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E.3Divide polynomials using synthetic division

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