Question:
Using factor theorem, show that g(x) is a factor of p(x), when
$p(x)=x^{4}-x^{2}-12, g(x)=x+2$
Solution:
Let:
$p(x)=x^{4}-x^{2}-12$
Here,
$x+2=0 \Rightarrow x=-2$
By the factor theorem, (x + 2) is a factor of the given polynomial if p (
Thus, we have:
$p(-2)=\left[(-2)^{4}-(-2)^{2}-12\right]$
$=(16-4-12)$
$=0$
Hence, (x + 2) is a factor of the given polynomial.
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