Using factor theorem, show that g(x) is a factor of p(x), when

Let:

$p(x)=2 x^{4}+9 x^{3}+6 x^{2}-11 x-6$

Here, 

$x-1=0 \Rightarrow x=1$

By the factor theorem, (x -">−- 1) is a factor of the given polynomial if p(1) = 0.
Thus, we have:

$p(1)=\left(2 \times 1^{4}+9 \times 1^{3}+6 \times 1^{2}-11 \times 1-6\right)$

$=(2+9+6-11-6)$

$=0$

Hence, $(x-1)$ is a factor of the given polynomial.