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

$p(x)=x^{4}-x^{2}-12, g(x)=x+2$

 

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 (2) = 0.
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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