Algebra Examples

$(x^{2} - 5 x + 4) (x^{2} - 9)$

Step 1

Factor $x^{2} - 5 x + 4$ using the AC method.

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Step 1.1

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 $4$ and whose sum is $- 5$ .

$- 4, - 1$

Step 1.2

Write the factored form using these integers.

$(x - 4) (x - 1) (x^{2} - 9)$

Step 2

Rewrite $9$ as $3^{2}$ .

$(x - 4) (x - 1) (x^{2} - 3^{2})$

Step 3

Factor.

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Step 3.1

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 $b = 3$ .

$(x - 4) (x - 1) ((x + 3) (x - 3))$

Step 3.2

Remove unnecessary parentheses.

$(x - 4) (x - 1) (x + 3) (x - 3)$