Question

For what values of b is the expression `x^2+bx+12` factorable?

Answer 1

`+-13, +-8, +-7`
These are the possible sums of the factor pairs of 12

Explanation:

b is the sum of the factors used to multiply to get 12 for the C value.

`( x + 1) xx (x + 12) = x^2 + 13 x + 12`
`( x - 1) xx (x - 12) = x^2 + (-13) x + 12`

`(x + 2) xx (x + 6) = x^2 + 8x + 12`
`(x - 2) xx (x - 6) = x^2 + (-8)x + 12`

`(x + 3) xx ( x+ 4) = x^2 + 7 x + 12`
`(x - 3) xx ( x -4) = x^2 + (-7) x + 12`

These are the only whole number factors of 12 which can be factored.