Operations with Polynomials
Aligned to A-APR.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
Add or subtract polynomials by combining like terms; multiply by distributing every term of one factor across the other. The result is always another polynomial.
Worked examples
Example 1
Multiply (x + 3)(x − 5). Distribute: x·x + x·(−5) + 3·x + 3·(−5) = x^2 − 5x + 3x − 15 = x^2 − 2x − 15.
Example 2
(x + 3)² is x² + 6x + 9, not x² + 9. The middle term is the one people drop.
Example 3
Polynomials are closed under addition, subtraction and multiplication, but not division: x ÷ (x+1) is not a polynomial.
Practice questions
- Add (2x^2 + 3x − 1) + (x^2 − 4x + 6).
- Subtract (5x − 2) − (3x + 7).
- Multiply (x + 4)(x + 2).
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
Operaciones con Polinomios
Suma o resta polinomios combinando términos semejantes; multiplica distribuyendo cada término de un factor sobre el otro. El resultado siempre es otro polinomio.
Ejemplo 1: Multiplica (x + 3)(x − 5). Distribuye: x·x + x·(−5) + 3·x + 3·(−5) = x^2 − 5x + 3x − 15 = x^2 − 2x − 15.
Ejemplo 2: (x + 3)² es x² + 6x + 9, no x² + 9. El término de en medio es el que la gente olvida.
Ejemplo 3: Los polinomios son cerrados bajo suma, resta y multiplicación, pero no bajo división: x ÷ (x+1) no es un polinomio.
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