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
- Find the zeros of (x−2)(x+5).
- Factor x² − 4 and state its zeros.
- 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.
▶ Watch this lessonEn 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.
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