Algebra Examples

$x^{4} - 11 x^{2} + 28$

Step 1

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

${(x^{2})}^{2} - 11 x^{2} + 28$

Step 2

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

$u^{2} - 11 u + 28$

Step 3

Factor $u^{2} - 11 u + 28$ using the AC method.

Tap for more steps...

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 $28$ and whose sum is $- 11$ .

$- 7, - 4$

Step 3.2

Write the factored form using these integers.

$(u - 7) (u - 4)$

Step 4

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

$(x^{2} - 7) (x^{2} - 4)$

Step 5

Rewrite $4$ as $2^{2}$ .

$(x^{2} - 7) (x^{2} - 2^{2})$

Step 6

Factor.

Tap for more steps...

Step 6.1

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 $b = 2$ .

$(x^{2} - 7) ((x + 2) (x - 2))$

Step 6.2

Remove unnecessary parentheses.

$(x^{2} - 7) (x + 2) (x - 2)$