Precalculus Examples

${(x^{2} - 14)}^{2} - 8 (x^{2} - 14) - 20$

Step 1

Let $u = x^{2} - 14$ . Substitute $u$ for all occurrences of $x^{2} - 14$ .

$u^{2} - 8 u - 20$

Step 2

Factor $u^{2} - 8 u - 20$ using the AC method.

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Step 2.1

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 $- 20$ and whose sum is $- 8$ .

$- 10, 2$

Step 2.2

Write the factored form using these integers.

$(u - 10) (u + 2)$

Step 3

Replace all occurrences of $u$ with $x^{2} - 14$ .

$(x^{2} - 14 - 10) (x^{2} - 14 + 2)$

Step 4

Simplify.

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Step 4.1

Subtract $10$ from $- 14$ .

$(x^{2} - 24) (x^{2} - 14 + 2)$

Step 4.2

Add $- 14$ and $2$ .

$(x^{2} - 24) (x^{2} - 12)$