What Is Factoring in Algebra?
Factoring a polynomial means breaking down an expression into a product of simpler polynomials or factors that, when multiplied together, produce the original polynomial.
The 4 Primary Factoring Methods
Greatest Common Factor (GCF)
Always factor out the GCF first: 6x² + 9x = 3x(2x + 3).
Difference of Squares
Formula: a² − b² = (a − b)(a + b). Example: x² − 16 = (x − 4)(x + 4).
Trinomial Factoring (x² + bx + c)
Find two numbers that multiply to c and add to b. Example: x² + 5x + 6 = (x + 2)(x + 3).
Factoring by Grouping
Used for 4-term polynomials: x³ + 3x² + 2x + 6 = x²(x + 3) + 2(x + 3) = (x² + 2)(x + 3).