Steps for Factoring Quadratic Expressions

Steps for Factoring Quadratic Expressions

1. Is the expression a binomial?

   • YES
     • Are the two terms in the binomial perfect squares with subtraction between them?
       • YES
         • Use difference of squares method
           • Bracket both terms together twice with opposite signs. Calculate the square root of each number. The answer will be the same terms in brackets with opposite signs.
       • NO
         • Factor out the GCF to simplify expression
   • NO
     • Is the factor a trinomial?
       • YES
         • Factor out GFC if possible first.
           • Is the factor a simple trinomial?
             • YES
               • USE SUM AND PRODUCT METHOD. Determine 2 numbers that multiply to get C and add to get B & write these numbers in binomials with the correct variables
             • NO
               • Is the factor a complex trinomial?
                 • YES
                   • Factor out GCF if possible
                     • Decide between decomposition method and trial and error/ inspection method.
                       • Trial and error/ Inspection method. Find two factors for the first number in the trinomial and two factors for the last number in the trinomial. Multiply diagonally. Add these 2 numbers together. Try different numbers until the number matches the coefficient of the middle term.
                         • use the first number listed as a factor for the first number in the trinomial and the first number listed as a factor for the third number in the trinomial and write the first binomial. Now use the second number listed as a factor for the first number in the trinomial and the second number listed as a factor for the last number in the trinomial and write the second binomial. : If the first term of the trinomial includes x it will be brought into the two binomials.
                           • Check your work by expanding out the binomial to see if the product of the two binomials is equal to the original trinomial.
                       • Find two numbers that add to (sum) B and multiply (product) to “ac" .Decompose (break down the middle term). Factor out the GCF in the first two terms and last two terms. Use the sign on the third term to decide which operation to use and rewrite the factor . Factor out the binomial in the bracket