Question

If $x^3+6x^2$ + 4x + k is exactly divisible by x + 2, then k =

• A. -6
• B. -7
• C. -8
• D. -10

Answer 1

The correct option is C

-8

f(x) $x^3+6x^2$ + 4x + k is divisible by x + 2

$\therefore$ Remainder = 0

Let x + 2 = 0, then x =-2 $\therefore$

f(-2) $=(-2{)}^3+6(-2{)}^2$ + 4(-2) + k

=-8+24-8+k=8+k

$\therefore$ 8+k = 0

$\Rightarrow$ k = - 8

$\therefore$ k = - 8