CCSS HSA-APR.B.2 Worksheets
Algebra 2 · Arithmetic with Polynomials & Rational Expressions
Know and apply the Remainder Theorem: for a polynomial p(x) and a number a, the remainder on division by (x - a) is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).
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Teaching guide
What students learn
Know and apply the Remainder Theorem: for a polynomial p(x) and a number a, the remainder on division by (x - a) is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).
Worked example
Use the Remainder Theorem to find the remainder when P(x) = x³ + 5x² + 4 is divided by (x + 4).
Answer: Remainder = 20
Why: By the Remainder Theorem the remainder equals P(-4) = 20. (Substitute x = -4 into P(x) using Horner's method; no long division needed.)
Generated and checked in code, so it is correct.
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