High School · Arithmetic with Polynomials and Rational Expressions

CCSS.MATH.CONTENT.HSA.APR.B.2

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).

Read this standard on the official Common Core site

Lessons that teach this standard

• The Rational Root Theorem: Finding Zeros of Polynomials

  List the possible rational zeros of a polynomial, test them with synthetic division, and use each zero you find to factor and solve the polynomial completely.

• The Remainder Theorem and the Factor Theorem

  Why dividing p(x) by x − a leaves the remainder p(a), why p(a) = 0 means x − a is a factor, and how the two theorems turn one known root into a full factorization.