High School · Arithmetic with Polynomials and Rational Expressions

CCSS.MATH.CONTENT.HSA.APR.B.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Read this standard on the official Common Core site

Lessons that teach this standard

• Factoring Polynomials: Cubes, Grouping and Quadratic Form

  Factor polynomials beyond quadratics: sums and differences of cubes, factoring by grouping, and polynomials in quadratic form, then use the factors to solve equations.

• The Fundamental Theorem of Algebra

  A polynomial of degree n has exactly n complex zeros, counted with multiplicity. Use that count and conjugate pairs to find every zero and build polynomials.

• Graphing Polynomial Functions: Zeros, Multiplicity and End Behavior

  How to sketch a polynomial from its factored form: where it crosses the x-axis, why a repeated factor makes it bounce, and how the leading term decides both ends.

• Polynomial and Rational Inequalities: Sign Charts

  Solve polynomial and rational inequalities with a sign chart: find every critical number, test each interval, and handle zeros of the denominator correctly.

• 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.