Master the four essential factoring techniques to solve any polynomial equation.
Technique 1: Greatest Common Factor (GCF)
Always extract the GCF first before attempting any other method. Divide every term by the largest shared number and lowest variable exponent.
Example: 6x³ + 9x² = 3x²(2x + 3)
Technique 2: Difference of Two Squares (DOTS)
Any expression of the form a² - b² factors cleanly into the product of conjugate binomials.
Formula: a² - b² = (a - b)(a + b) | Example: 16x² - 81 = (4x - 9)(4x + 9)
Technique 3: Factoring Quadratic Trinomials (x² + bx + c)
Find two numbers p and q that multiply to 'c' (p · q = c) and add up to 'b' (p + q = b).
Example: x² - 7x + 12 = (x - 3)(x - 4) [since -3 × -4 = 12 and -3 + -4 = -7]
Technique 4: Factoring by Grouping (4-Term Polynomials)
Group terms into pairs, factor the GCF from each pair, and extract the common binomial factor.
Example: x³ + 3x² + 2x + 6 = x²(x + 3) + 2(x + 3) = (x² + 2)(x + 3)
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