CurriculumGrade 11Mathematics

Zeros and Factors of Polynomials

Aligned to A-APR.B.3 — Common Core State Standards for Mathematics.

What this lesson teaches

The zeros of a polynomial are the x-values where it equals 0 — its factors reveal them, and they are where the graph crosses the x-axis.

Worked example

f(x) = x³ − x = x(x−1)(x+1). Zeros at x = 0, 1, −1, so the graph crosses the x-axis at those three points.

Practice questions

  1. Find the zeros of (x−2)(x+5).
  2. Factor x² − 4 and state its zeros.
  3. How many real zeros can a cubic have at most?

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Ceros y Factores de Polinomios

Los ceros de un polinomio son los valores de x donde es igual a 0 — sus factores los revelan, y son los puntos donde la gráfica cruza el eje x.

Ejemplo: f(x) = x³ − x = x(x−1)(x+1). Ceros en x = 0, 1, −1, por lo que la gráfica cruza el eje x en esos tres puntos.

More Algebra lessons

Rewriting Expressions (Completing the Square)A-SSE.B.3Sum of a Finite Geometric SeriesA-SSE.B.4The Remainder TheoremA-APR.B.2Proving Polynomial IdentitiesA-APR.C.4Rewriting Rational ExpressionsA-APR.D.6Creating Equations to Model ProblemsA-CED.A.1

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