Zeros 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 — they are the x-intercepts of its graph. Factor, set each factor equal to 0, and solve to find them.
Worked examples
Example 1
Find the zeros of y = (x − 1)(x + 4). Set each factor to 0: x − 1 = 0 gives x = 1, and x + 4 = 0 gives x = −4. The graph crosses the x-axis at (1, 0) and (−4, 0).
Example 2
y = (x − 2)² has a repeated zero at x = 2 — the graph touches the axis there and turns back instead of crossing.
Example 3
A degree-n polynomial has at most n real zeros, and may have fewer. x² + 1 has none.
Practice questions
- Find the zeros of y = (x + 2)(x − 6).
- Find the zeros of y = x(x − 3).
- Factor y = x^2 − x − 12 and give its zeros.
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 de Polinomios
Los ceros de un polinomio son los valores de x donde vale 0: son las intersecciones con el eje x de su gráfica. Factoriza, iguala cada factor a 0 y resuelve para hallarlos.
Ejemplo 1: Halla los ceros de y = (x − 1)(x + 4). Iguala cada factor a 0: x − 1 = 0 da x = 1, y x + 4 = 0 da x = −4. La gráfica corta el eje x en (1, 0) y (−4, 0).
Ejemplo 2: y = (x − 2)² tiene un cero repetido en x = 2 — la gráfica toca el eje ahí y regresa en vez de cruzarlo.
Ejemplo 3: Un polinomio de grado n tiene a lo más n ceros reales, y puede tener menos. x² + 1 no tiene ninguno.
More Algebra lessons
Teach this lesson today
An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.
Start free — no card required