m^2-12m+20

Question

Factor the trinomial.

Answer 1

To answer this question, it is helpful to understand how the FOIL method works to multiply polynomials.  Basically you need to write the answer in the form of (m + number1)(m + number2).  You find number1 and number2 by knowing that the two numbers need to add to -12, but multiply to 20.  Two numbers that do this are -2 and -10.  So factorizing results in the answer (m - 2)(m - 10).  You can apply FOIL to redo the multiplication to double check that you get m^2 -12 m + 20.

Answer 2

m² - 12m + 20

 

We need two numbers that add to -12 and multiply to give 20.  Let's try a few:

 

                Multiply to:       Add to:

5 and 4          20                   9

-5 and -4       20                  -9

10 and 2        20                  12

-10 and -2     20                  -12    This is the combination!

 

m² - 12m + 20 = (m-10)(m-2)