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

Let:

$p(x)=2 x^{3}+7 x^{2}-24 x-45$

Now,

$x-3=0 \Rightarrow x=3$

By the factor theorem, (x -">−- 3) is a factor of the given polynomial if p(3) = 0.
Thus, we have:

$p(3)=\left(2 \times 3^{3}-7 \times 3^{2}-24 \times 3-45\right)$

$=(54+63-72-45)$

$=0$

Hence, (x -">−- 3) is a factor of the given polynomial.