Which of the following is one of the factors of

$(x^{4} + x^{2} - 20)$

$(x^{2} - 5)$

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$(x^{2} + 4)$

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$(x - 4)$

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$(x^{2} + 5)$

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Solution

The correct option is D
$(x^{2} + 5)$

$(x^{4} + x^{2} - 20)$

Let $x^{2} = t$

$\Rightarrow t^{2} + t - 20$

$\Rightarrow t^{2} + 5 t - 4 t - 20$

$\Rightarrow t (t + 5) - 4 (t + 5)$

$\Rightarrow (t + 5) (t - 4)$

Substituting the value of t

$\Rightarrow (x^{2} + 5) (x^{2} - 4)$

$\Rightarrow (x^{2} + 5) (x - 2) (x + 2)$

Suggest Corrections

Similar questions

x^{4} + x^{2} - 20

x^{2} + 5

The factors of $x^{4} + x^{2} + 25$ are

x^{2} + \frac{1}{x^{2}} + 2 - 2 x - \frac{2}{x}

x^{4} + 4

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