Question

Using factor theorem, show that g(x) is a factor of p(x), when
$p\left(x\right)=2x^3+7x^2-24x-45,g\left(x\right)=x-3$

Answer 1

Let:

$p\left(x\right)=2x^3+7x^2-24x-45g\left(x\right)=x-3x=3$

By the factor theorem, (x - 3) is a factor of the given polynomial if p(3) = 0.

Thus, we have:

$p\left(2\right)=2\times 3^3-7\times 3^2-24\times 3-45=54+63-72-45=0$

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