Question

Determine which of the following polynomials has $(x-2)$ a factor :

$4x^2+x-2$

Answer 1

STEP 1 : Determining whether polynomial has $(x-2)$ a factor or not

Let $p\left(x\right)=4x^2+x-2$ be the polynomial

By factor theorem

If $p\left(x\right)$ is a polynomial of degree $n>1$ and $a$ is any real number, then $x–a$ is a factor of $p\left(x\right)$, if $p\left(a\right)=0$,

Therefore, $(x-2)$ is a factor of $p\left(x\right)$, if $p\left(2\right)=0$

$p\left(x\right)=4x^2+x-2$

$p\left(2\right)=4\times {\left(2\right)}^2+2-2$

$p\left(2\right)=4\times 4+2-2$

$p\left(2\right)=16$

Since, $p\left(2\right)\ne 0$

Hence, $(x-2)$ is not a factor of polynomial $4x^2+x-2$.