Factor x^2 - 13x + 42

Question

Factoring this problem is difficult 

Answer 1

x² - 13x + 42 = (x+a)(x+b)

 

You want two numbers, a and b, that multiply to give 42 (a*b = 42) and add to give -13 (a+b = -13).  Since the numbers must add to give a negative number and multiply to give a positive number, they most both be negative.  Let's try some factors of 42:

 

-21 * -2 = 42           -21 + -2 = -23

-14 * -3 = 42           -14 + -3 = -17

-13 * -4 = 42           -13 + -4 = -17

 -7 * -6 = 42           -7 + -6 = -13  So this is the answer!

 

x² - 13x + 42 = (x-7)(x-6)