Factor x^4-9x^2+18

$x^{4} - 9 x^{2} + 18$

Step 1

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

${(x^{2})}^{2} - 9 x^{2} + 18$

Step 2

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

$u^{2} - 9 u + 18$

Step 3

Factor $u^{2} - 9 u + 18$ using the AC method.

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 $18$ and whose sum is $- 9$ .

$- 6, - 3$

Write the factored form using these integers.

$(u - 6) (u - 3)$

Step 4

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

$(x^{2} - 6) (x^{2} - 3)$

Factor x^4-9x^2+18

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