How do you factor each polynomial x^2+7x+12 and problem number 2 x^2+8x-20?

Question

How do you factor each polynomial x^2+7x+12 and problem number 2 x^2+8x-20?

Answer 1

Assume the first polynomial factors as (x + a)(x + b).  You know that ab = 12 so either both a and b are positive or both a and b are negative.  You know that a + b = 7 so then both a and b are positive.  

x² + 7x + 12 = (x + 3)(x + 4)

Assume the second polynomial factors as (x + a)(x + b).  You know that ab = -20 so either a is positive and b is negative or visa versa.  You know that a + b  = 8.  Since a = 10 and b = -2 satisfies both of these conditions, the polynomial factors as:

x² + 8x - 20 = (x + 10)(x - 2)

Hope this helps you!