Factor x^4-7x^2+12 - MathMaster

$x^{4} - 7 x^{2} + 12$

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

${(x^{2})}^{2} - 7 x^{2} + 12$

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

$u^{2} - 7 u + 12$

Factor $u^{2} - 7 u + 12$ 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 $12$ and whose sum is $- 7$ .

$- 4, - 3$

Write the factored form using these integers.

$(u - 4) (u - 3)$

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

$(x^{2} - 4) (x^{2} - 3)$

Rewrite $4$ as $2^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

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

Factor x^4-7x^2+12

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