Question

f($x$) = $x^2+kx+6$.
If ($x-2$) is a factor of f($x$), then the value of k = .

• A. 5
• B. -5
• C. 4
• D. -4

Answer 1

The correct option is B -5

According to the factor theorem,
if ($x-a$) is a factor of a polynomial
f($x$), then f(a) = 0.
Given, ($x-2$) is a factor of f($x$), then f(2) = 0.
$\Rightarrow$ f(2) = $2^2+k\times 2+6=0$
$\Rightarrow 4+2k+6=0$
$\Rightarrow 2k=-10$
$\Rightarrow k=-5$