Question

If $(x-1)$ is a factor of $x^2+2x-k$, then find $k$.

• A. $-3$
• B. $3$
• C. $2$
• D. $-2$

Answer 1

The correct option is B $3$

According to factor theorem, if $(x-a)$ is a factor of $f\left(x\right)$, then $f\left(a\right)=0$

Given that $(x-1)$ is a factor of $f\left(x\right)=x^2+2x-k$

$\therefore f\left(1\right)=0$

$\Rightarrow 1^2+2\left(1\right)-k=0$

$\Rightarrow 3-k=0$

$\Rightarrow k=3$

Hence, if $(x-1)$ is a factor of $x^2+2x-k$, then the value of $k$ is $3$