ANSWER
The correct answer is C.
EXPLANATION
The given polynomial has equation
[tex]p(b) = {b}^{3} + 3 {b}^{2} - b + 12[/tex]
According to the Remainnder Theorem, if (b+4) is a factor of p(b) = b³+3b²-b+12 then
[tex]p( - 4) = 0[/tex]
We now substitute b=-4 to check.
[tex]p( - 4) = {( - 4)}^{3} + 3 {( - 4)}^{2} - ( - 4) + 12 [/tex]
[tex]p( - 4) = - 64+ 48 + 4 + 12 [/tex]
Simplify:
[tex]p( - 4) = - 16 + 16 = 0[/tex]
Since p(-4) is zero, (b+4) is a factor of p(b) = b³+3b²-b+12.
The correct choice is C.
