Precalculus Examples

${(x - 4)}^{2} + 3 (x - 4) - 18$

Step 1

Let $u = x - 4$ . Substitute $u$ for all occurrences of $x - 4$ .

$u^{2} + 3 u - 18$

Step 2

Factor $u^{2} + 3 u - 18$ 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 $- 18$ and whose sum is $3$ .

$- 3, 6$

Step 2.2

Write the factored form using these integers.

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

Step 3

Replace all occurrences of $u$ with $x - 4$ .

$(x - 4 - 3) (x - 4 + 6)$

Step 4

Simplify.

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Step 4.1

Subtract $3$ from $- 4$ .

$(x - 7) (x - 4 + 6)$

Step 4.2

Add $- 4$ and $6$ .

$(x - 7) (x + 2)$