Question

If x−1 is a factor of x2+4x+a and x−2 is a factor of x2+4x+b, then a+b = .

• A. -17
• B. -12
• C. -5
• D. -60

Answer 1

The correct option is A -17

According to the factor theorem, if $x-a$ is a factor of a polynomial f($x$), then f(a) = 0.
Since, ($x-1$) is a factor of $x^2+4x+a$ ,
$\Rightarrow$ $1^2+4\times 1+a$ = 0
$\Rightarrow$ a = -5
Since, ($x-2$) is a factor of $x^2+4x+b$,
$\Rightarrow$ $2^2+4\times 2+b$ = 0
$\Rightarrow$ b = -12

Hence, a+b = -5 + -12 = -17.