Factoring Techniques Flashcards

Grade 10 · Math · Flashcards

All the key factoring patterns and methods for 10th grade algebra.

Flashcards

Greatest Common Factor (GCF): The largest factor shared by all terms; always factor this out FIRST
Factoring x² + bx + c: Find p, q where p·q = c and p + q = b; write (x + p)(x + q)
Difference of squares: a² - b² = (a + b)(a - b)
Sum of squares: a² + b² — prime over real numbers; cannot be factored
Perfect square trinomial (add): a² + 2ab + b² = (a + b)²
Perfect square trinomial (subtract): a² - 2ab + b² = (a - b)²
Sum of cubes: a³ + b³ = (a + b)(a² - ab + b²)
Difference of cubes: a³ - b³ = (a - b)(a² + ab + b²)
Factoring by grouping: Group 4-term polynomial in pairs, factor each pair, then factor the common binomial
AC method for ax² + bx + c: Multiply a·c, find factors of a·c that add to b, split middle term, factor by grouping
Prime polynomial: Cannot be factored over the integers; like a prime number
Verifying factoring: Multiply the factors back out — result must match the original polynomial
Zero product property: If (A)(B) = 0, then A = 0 or B = 0; used to solve equations after factoring
Factoring strategy order: 1. GCF 2. # of terms (2→diff of squares, 3→trinomial, 4→grouping) 3. Verify