Which of the binomials below is a factor of this trinomial x^2+12x+32
a. x+2
b. x-4
c. x-2
d. x+4

If we were to factor it
what 2 numbers multiply to 32 and addd to 12
8 and 4
(x+8)(x+4)
both signs are positive since all signs in equation are positive

so D is the correct answe

we can use eliminateion also to find the answer

we see that the sign of x^2 and 12x and 32 are both positive, so the signs of the factors also must be positive (can't be B or C)
then, we need to find what 2 numbers multiply to get 32 and add to 12
if we picked 2 (for A), then 2 times 16=32, but 2+16≠12
4 times 8=32 and 4+8=12 so it must be D