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Polynomials — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsPolynomials2 Marks
Question
Using factor theorem, show that $g(x)$ is a factor of $p(x)$, when$\text{p}(\text{x})=2\sqrt2\text{x}^2+5\text{x}+\sqrt2,$ $\text{g}(\text{x})=\text{x}+\sqrt2$
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Answer

$\text{p}(\text{x})=2\sqrt2\text{x}^2+5\text{x}+\sqrt2,$By the factor theorem, $(x - a)$ will be factor of $p(x)$ if $p(a) = 0.$
Here, $\text{f}(-\sqrt{2})=2\sqrt2(-\sqrt2)^2+5(-\sqrt2)+\sqrt2$
$=2\sqrt2\times2-5\sqrt2+\sqrt2$
$=4\sqrt2-5\sqrt2+\sqrt2$
$=5\sqrt2-5\sqrt2=0.$
$\therefore(\text{x}+\sqrt2)$ is a factor of $2\sqrt2\text{x}^2+5\text{x}+\sqrt2.$

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