Question

If x + 2 is a factor of $x^2$ + mx + 14, then m =

• A. 7
• B. 2
• C. 9
• D. 14

Answer 1

The correct option is C

9

x+ 2 is a factor of f(x) = $x^2$ + mx + 14

Let x + 2 = 0, then x=-2

$\therefore$ f(-2) $=(-2{)}^2$ + m(-2) + 14

= 4-2m+ 14= 18-2m

$\therefore$ x + 2 is a factor of f(x)

$\therefore$ Remainder = 0

$\Rightarrow$ 18-2m=0

2m= 18 $\Rightarrow =\frac{18}{2}=9$