A.APR

Arithmetic with Polynomials and Rational Expressions

A.APR.1(9/10) Add, subtract, and multiply polynomials.A.APR.2(11) Factor higher degree polynomials; identifying that some polynomials are prime.A.APR.3(11) Know and apply the Remainder Theorem: For a polynomial p(x) and a number c, the remainder on division by (x - c) is p(c), so p(c) = 0 if and only if (x - c) is a factor of p(x).A.APR.4(9/10/11) Generate polynomial identities from a pattern. For example, difference of squares, perfect square trinomials, (emphasize sum and difference of cubes in grade 11).A.APR.5(+) Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle. The Binomial Theorem can be proven by mathematical induction or by a combinatorial argument.A.APR.6(+) Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.A.APR.7(+) Add, subtract, multiply, and divide rational expressions.
Goblins

1-on-1 AI tutoring aligned to A.APR. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.

Free for teachers, forever →