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Polynomials — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsPolynomials2 Marks
Question
Using factor theorem, show that $g(x)$ is a factor of $p(x)$, when
$p(x)=x^4-x^2-12, g(x)=x+2$
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Answer

$f(x)=\left(x^4-x^2-12\right)$
By the Factor Theorem, $(x+2)$ will be a factor off $(x)$ if $f(-2)=0$.
Here, $f(-2)=(-2)^4-(-2)^2-12$
$=16-4-12$
$=16-16=0$
$\therefore(x+2)$ is a factor of $\left(x^4-x^2-12\right)$.

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