Algebra Examples

$x^{4} + x^{2} - 30$

Step 1

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

${(x^{2})}^{2} + x^{2} - 30$

Step 2

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

$u^{2} + u - 30$

Step 3

Factor $u^{2} + u - 30$ using the AC method.

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Step 3.1

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 $- 30$ and whose sum is $1$ .

$- 5, 6$

Step 3.2

Write the factored form using these integers.

$(u - 5) (u + 6)$

Step 4

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

$(x^{2} - 5) (x^{2} + 6)$