Question

# Let f(x) be a polynomial such that $f\left( \dfrac{-1}{2} \right)=0$ , then a factor of f(x) isA. 2x-1B. 2x+1C. x-1D. x+1

Now, we know that on putting $x=\left( \dfrac{-1}{2} \right)$, the function becomes zero that is $f\left( \dfrac{-1}{2} \right)=0$ which means $x=\left( \dfrac{-1}{2} \right)$ is a zero of the polynomial f(x), hence, we can write as follows
$\left( x+\dfrac{1}{2} \right)$ is a factor of f(x) which can also be represented as follows