Precalculus Examples

$x^{4} + 9 x^{2} + 20$

Step 1

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

${(x^{2})}^{2} + 9 x^{2} + 20$

Step 2

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

$u^{2} + 9 u + 20$

Step 3

Factor $u^{2} + 9 u + 20$ 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 $20$ and whose sum is $9$ .

$4, 5$

Step 3.2

Write the factored form using these integers.

$(u + 4) (u + 5)$

Step 4

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

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