Question

Factor. w2 + 12w - 13

Answer 1

Remember that the product of two binomials on a single variable is a trinomial of the form:

$(w+a)(w+b)=w^2+(a+b)w+ab$

Comparing with the coefficients of the trinomial:

$w^2+12w-13$

We should find two numbers a and b such that a+b=12 and a*b=-13.

Since the product a*b is negative, one number should be negative and the other should be positive. Notice that 13+(-1)=12 and (13)(-1)=-13. Then those numbers are 13 and -1. Therefore:

$w^2+12w-13=(w+13)(w-1)$