Always check for a GCF first! It's the largest term that divides into every term of the polynomial.
Example: Factor 6x³ + 9x² → 3x²(2x + 3)
Applies to binomials of the form a² - b². It factors into (a - b)(a + b).
Example: Factor x² - 25 → (x - 5)(x + 5)
Find two numbers that multiply to c and add to b.
Example: Factor x² - 5x + 6 → (x - 2)(x - 3)
When 'a' is not 1, use the "AC Method" or "Grouping".
Example: Factor 2x² + 7x + 3 → (x + 3)(2x + 1)
Formulas: a³ + b³ = (a + b)(a² - ab + b²) and a³ - b³ = (a - b)(a² + ab + b²)
Example: Factor x³ - 8 → (x - 2)(x² + 2x + 4)
Used for polynomials with four terms. Group terms and find a GCF for each pair.
Example: Factor x³ + 2x² + 3x + 6 → (x² + 3)(x + 2)