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## Algebra II (2018 edition)

### Course: Algebra II (2018 edition)>Unit 3

Lesson 5: Practice dividing polynomials with remainders

# Divide polynomials with remainders

## Problem

Let a, left parenthesis, x, right parenthesis, equals, 5, x, cubed, minus, 6, x, squared, minus, 8, x, plus, 9, and b, left parenthesis, x, right parenthesis, equals, x, start superscript, 4, end superscript, plus, 2, x, cubed, plus, x, plus, 1.
When dividing a by b, we can find the unique quotient polynomial q and remainder polynomial r that satisfy the following equation:
start fraction, a, left parenthesis, x, right parenthesis, divided by, b, left parenthesis, x, right parenthesis, end fraction, equals, q, left parenthesis, x, right parenthesis, plus, start fraction, r, left parenthesis, x, right parenthesis, divided by, b, left parenthesis, x, right parenthesis, end fraction,
where the degree of r, left parenthesis, x, right parenthesis is less than the degree of b, left parenthesis, x, right parenthesis.
What is the quotient, q, left parenthesis, x, right parenthesis?
q, left parenthesis, x, right parenthesis, equals
What is the remainder, r, left parenthesis, x, right parenthesis?
r, left parenthesis, x, right parenthesis, equals
Stuck?
Stuck?