Question:
Using factor theorem, show that g(x) is a factor of p(x), when
$p(x)=2 x^{3}+7 x^{2}-24 x-45, g(x)=x-3$
Solution:
Let:
$p(x)=2 x^{3}+7 x^{2}-24 x-45$
Now,
$x-3=0 \Rightarrow x=3$
By the factor theorem, (x
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
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