How Do You Factor Polynomials?

Factoring a four-term polynomial can be complicated. It uses the same procedure for factoring a three-term polynomial but requires a few more steps.

  1. Factor by grouping

    Grouping is the easiest way to factor a four-term polynomial. Use the polynomial 2x³ - 8x² - 3x + 12 as the example. First, group 2x³ - 8x² and -3x + 12 as two separate equations. Factor 2x³ - 8x² by finding the greatest common factor, which is 2x². Using the greatest common factor, 2x³ - 8x² becomes 2x²(x - 4). Now do the other group, -3x + 12. The greatest common factor for that equation is -3. Using the greatest common factor, -3x + 12 becomes -3(x - 4). Put it back together, and you get: 2x²(x - 4) - 3(x - 4). Find the greatest common factor for this equation as well, which is (x - 4). Using the greatest common factor, you get (x - 4)(2x² - 3).

  2. Factor by grouping

    After the grouping, there should always be two terms that are the same. If this isn't the case, then either the grouping was done incorrectly, the polynomial cannot be factored, or it has decimals.

  3. Check your answer

    Check to see if the answer is correct by doing the math: (x - 4)(2x² - 3) Using the FOIL (First, Outer, Inner, Last) method, use x and multiply it by the two terms on the right side. Then, use -4 to multiply the right side again: 2x³ - 3x - 8x² + 12 Rearrange the equation based on the higher exponents to 2x³ - 8x² - 3x + 12, which proves that the answer is correct.