Question

Please answer

Answer 1

ANSWER

The correct answer is C.

EXPLANATION

The given polynomial has equation

$p(b) = {b}^{3} + 3 {b}^{2} - b + 12$

According to the Remainnder Theorem, if (b+4) is a factor of p(b) = b³+3b²-b+12 then

$p( - 4) = 0$

We now substitute b=-4 to check.

$p( - 4) = {( - 4)}^{3} + 3 {( - 4)}^{2} - ( - 4) + 12$

$p( - 4) = - 64+ 48 + 4 + 12$

Simplify:

$p( - 4) = - 16 + 16 = 0$

Since p(-4) is zero, (b+4) is a factor of p(b) = b³+3b²-b+12.

The correct choice is C.