Question

Using factor theorem, show that:
(x − 3) is a factor of (2x³ + 7x² − 24x − 45)

Answer 1

Let:
$f\left(x\right)=2x^3+7x^2-24x-45$
Now,
$x-3=0\Rightarrow x=3$
By the factor theorem, (x $-$ 3) is a factor of the given polynomial if f(3) = 0.
Thus, we have:
$$\begin{gathered} f\left(3\right)=\left(2\times 3^3-7\times 3^2-24\times 3-45\right) \\ =\left(54+63-72-45\right) \\ =0 \end{gathered}$$
Hence, (x $-$ 3) is a factor of the given polynomial.