Factor x^4-5x^2-24 - MathMaster

$x^{4} - 5 x^{2} - 24$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

${(x^{2})}^{2} - 5 x^{2} - 24$

Let $u = x^{2}$ . Substitute $u$ for all occurrences of $x^{2}$ .

$u^{2} - 5 u - 24$

Factor $u^{2} - 5 u - 24$ using the AC method.

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Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 24$ and whose sum is $- 5$ .

$- 8, 3$

Write the factored form using these integers.

$(u - 8) (u + 3)$

Replace all occurrences of $u$ with $x^{2}$ .

$(x^{2} - 8) (x^{2} + 3)$

Factor x^4-5x^2-24

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