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How to Factor Polynomials

Factoring is the opposite of distributing. If you can find a common factor, you can reduce an expression.


  • Step 1: Find the greatest common factor Look at the expression and find the greatest common factor for each term. For the expression 2x2 + 4x, both terms contain factors of 2 and factors of x.
  • Step 2: Factor out greatest common factor Remove the largest factors common shared by each term – 2 and x – and place them outside a set of empty parentheses.
  • Step 3: Determine what GCF is multiplied with Determine the greatest common factor of each term of the expression. In the example, it's 2x. Then, determine what it is multiplied with to equal the original two terms and place those terms inside the parentheses. 2x times x equals 2x2, and 2x times 2 equals 4x.
  • TIP: Remember the distributive law ab + ac = a(b + c).
  • Step 4: Find the difference of squares Finding the difference of two squares is another type of factoring. In the expression x2 – 4, x2 is the square of x and 4 is the square of 2.
  • Step 5: Make parentheses To factor the difference of two squares, draw two sets of parentheses. On the left side of each set of parentheses, split the first square, x2, into two x's.
  • TIP: Since this is a difference of squares, it only works when one term is being subtracted from another. You cannot factor the sum of two squares.
  • Step 6: Split second square Write the second square in the right side of the parentheses. Since the second term is being subtracted, each set of parentheses must have a different sign.
  • FACT: Babylonians used a number system with a base of 60 rather than the standard system with a base of 10 we use today.

You Will Need

  • A polynomial
  • A pencil
  • Paper

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