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

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

$p(x)=2 x^{3}+9 x^{2}-11 x-30, g(x)=x+5$

Solution:

Let:

$p(x)=2 x^{3}+9 x^{2}-11 x-30$

Here,

$x+5=0 \Rightarrow x=-5$

By the factor theorem, (x + 5) is a factor of the given polynomial if p (5) = 0.
Thus, we have:

$p(-5)=\left[2 \times(-5)^{3}+9 \times(-5)^{2}-11 \times(-5)-30\right]$

$=(-250+225+55-30)$

$=0$

Hence, (x + 5) is a factor of the given polynomial.