Polynomials and Factoring Flashcards

Grade 9 · Math · Flashcards

Key vocabulary, patterns, and worked examples for mastering polynomial factoring techniques.

Flashcards

Monomial: A polynomial with exactly one term, e.g., 5x³
Binomial: A polynomial with exactly two terms, e.g., x² − 4
Trinomial: A polynomial with exactly three terms, e.g., x² + 5x + 6
Standard form of a polynomial: Terms written in descending order of degree, e.g., 4x³ − 2x² + x − 7
Difference of squares formula: a² − b² = (a + b)(a − b)
Perfect square trinomial (positive): a² + 2ab + b² = (a + b)²
Perfect square trinomial (negative): a² − 2ab + b² = (a − b)²
Factor by grouping (4 terms): Group pairs, factor each pair's GCF, then factor the common binomial. e.g., x³ + 2x² + 3x + 6 = (x² + 3)(x + 2)
AC method for ax² + bx + c: Multiply a·c, find factor pair summing to b, split middle term, factor by grouping
Verify a factored polynomial: Expand the factors using FOIL or distribution and confirm you recover the original polynomial
Factor 9x² − 1: (3x + 1)(3x − 1) — difference of squares with a = 3x, b = 1
Factor x⁴ − 16: (x² + 4)(x + 2)(x − 2) — apply difference of squares twice
Zero Product Property: If ab = 0, then a = 0 or b = 0; used to solve equations after factoring
Prime polynomial: A polynomial that cannot be factored over the integers, e.g., x² + 4