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A-APR.2 Warmup M3-002-A04-V01

Apply the Remainder Theorem to connect p(a), remainders, and factors x-a.

Use polynomial long division to find the remainder from a linear divisor

Problem

Use the polynomial long-division setup to find the remainder when \(x^3~+~2x^2~-~5\) is divided by \(x~-~1\).

Unsolved polynomial long division with divisor x − 1 and dividend x³ + 2x² + 0x − 5. The quotient line is blank; the zero coefficient preserves the missing x term. Open full size
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What this problem is really about

Polynomial long division works by canceling the current leading term over and over. We’ll first insert a zero x term to keep the powers aligned, then repeat divide, multiply back, and subtract until what remains has lower degree than x minus 1. That leftover constant is the remainder.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
A-APR.2
Category
Algebra
Domain
Arithmetic with Polynomials and Rational Expressions
Objective
Apply the Remainder Theorem to connect p(a), remainders, and factors x-a.
Problem type
Use polynomial long division to find the remainder from a linear divisor