Determine which of the following binomials is a factor of h^3-8h^2+19h-12 .
A. h + 2
B. h - 4
C. h + 6
D. h + 4

To find the answer, we can use the remainder theorem.

If the binomial is a factor, it will be able to divide the equation with no remiander,making the outcome = 0.

The remainder theorem is to substitute the factor into the equation.

We can try it one by one:

A.h + 2
h= -2

f(-2)=(-2)^3-8(-2)^2+19(-2)-12
=-8+32-38-12
=-24
≠0

A is incorrect.

B. h-4
h=4

f(4)=(4)^3-8(4)^2+19(4)-12
=64-128+76-12
= 0

Therefore B. h-4 is the correct answer.

Hope it helps!