Decorative ribbon image.

Long Division of Polynomials

Polynomial Long Division top left imagePolynomial Long Division top right image
HomeAlgebraPolynomials

Polynomial long division is similar to long division of basic math, however polynomials have multiple terms.

How to Solve a Polynomial Division Math Problem

When we use long division math:

Quotient and Remainder

Divisor / Dividend

 2 R 1

3 / 7

− 6

 1

The answer is 2 + Remainder.

Remainder = 1/3, therefore the answer is 2 + 1/3 or 2 1/3.

To prove this:

3 (2 + 1/3) = 6 + 1 = 7

Use the same approach for division of polynomials.

Polynomial Long Division visualized.

Polynomial long division similar to basic math.

To solve a polynomial division problem:

(2x3 − 7x + 2) / (x2 + x − 1)

f(x) = 2x3 − 7x + 2 (dividend)

g(x) = x2 + x − 1 (divisor)

q(x) = quotient and remainder

There are multiple terms to consider, proceed term-by-term.

The math term of the dividend having the highest degree is 2x3

Find a multiple of x2 equal or as close as possible to 2x3

(x2) (2x) = 2x3

Write the term as the first term of the quotient:

 2x

x2 + x − 1 / 2x3 − 7x + 2

Next, multiply each term of the divisor by the 2x and write it beneath the dividend:

 2x

x2 + x − 1 / 2x3 − 7x  + 2

2x3 + 2x2 − 2x

The divisor does not have a second degree term. Insert a zero term:

 2x

x2 + x − 1 / 2x3 + 0x2 − 7x + 2

−(2x3 + 2x2 − 2x)

−2x2 − 5x + 2

Subtract from divisor

Apply the same steps to find a quotient term of −2x2:

(x2) (−2) = (−2x2)

Write the term as the second term of the quotient and multiply each term of the divisor by the (−2) and write it beneath the dividend:

 2x 2

x2 + x − 1 / 2x3 + 0x2 − 7x + 2

−(2x3 + 2x2 − 2x)

−2x2 − 5x + 2

Subtract from divisor

−(−2x2 − 2x + 2)

−3x

Remainder

Thus, q(x) = 2x − 2 with a Remainder of −3x

Top of Page

Copyright © DigitMath.com

All Rights Reserved.

AboutPrivacy