For what 6 values of b is the expression factorable?

Question

This is for my class homework and I really don´t understand it. For what 6 values of b is the expression factorable? x^2+bx+12

Answer 1

List all the factors of 12 (both + and -)

recognize that any combination must have the same sign---because 12 is positive. For the same reason, b is always a SUM

List all the unique combinations, and add them to get the b value

Answer 2

x² + 13x + 12 = (x + 1)(x + 12)

x² + 8x +12 = (x + 2)(x + 6)

x² +7x + 12 = (x + 3)(x + 4)

x² - 13x + 12 = (x - 1)(x - 12)

x² - 8x + 12 = (x - 2)(x - 6)

x² - 7x + 12) = (x - 3)(x - 4)

As a student in pre-calculus you should be more familiar with the roles of various numbers in the product of a two binomials.