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Factoring a polynomial is the opposite process of multiplying polynomials. Recall that when we factor a number, we are looking for prime factors that multiply together to give the number; for example

6 = 2 × 3 , or 12 = 2 × 2 × 3.

When we factor a polynomial, we are looking for simpler polynomials that can be multiplied together to give us the polynomial that we started with. You might want to review multiplying polynomials if you are not completely clear on how that works.

When we factor a polynomial, we are usually only interested in breaking it down into polynomials that have integer coefficients and constants.