Math III · A-APR.4

Prove polynomial identities and use them to solve or describe numerical relationships.

Prove polynomial identities and use them to solve or describe numerical relationships.

Concept Algebra
Domain Arithmetic with Polynomials and Rational Expressions
Problem Types

Problem Templates In This Objective

14 problem types are attached to this objective. The full web app handles practice, answers, hints, and walkthroughs.

Template 1

Verify a polynomial identity by expanding and comparing both sides

4 variants
Template 2

Expand a binomial square completely

4 variants
Template 3

Verify and apply the difference-of-squares identity

4 variants
Template 4

Verify and apply the sum-of-cubes and difference-of-cubes identities

4 variants
Template 5

Use a polynomial identity for fast mental computation

4 variants
Template 6

Factor a polynomial by recognizing a special identity

4 variants
Template 7

Use a factoring identity to solve a polynomial equation

4 variants
Template 8

Match a polynomial identity to labeled component areas or volumes

4 variants
Template 9

Complete a missing term in a polynomial identity by expanding and comparing coefficients

4 variants
Template 10

Decide whether a polynomial equation is an identity by expanding both sides and comparing

4 variants
Template 11

Factor an expression using a polynomial identity

4 variants
Template 12

Simplify a rational identity while preserving original-domain exclusions

4 variants
Template 13

Decide whether a polynomial equation is an identity by expanding both sides

4 variants
Template 14

Identify which polynomial identity matches a given expression

4 variants