Question

If $(x-1)$ is a factor of $(2x^4+9x^3+6x^2-11x-a)$, find $a$.

Answer 1

Given that, $(x-1)$ is a factor of $2x^4+9x^3+6x^2-11x-9$

To find out: The value of $a$.

Let the given polynomial be $p\left(x\right)$.

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

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

$\Rightarrow 2(1{)}^4+9(1{)}^3+6(1{)}^2-11(1)-a=0$

$\Rightarrow 2+9+6-11-a=0$

$\Rightarrow a=6$

Hence, the value of $a$ is $6$.