Factor a^4-4a^2-21

$a^{4} - 4 a^{2} - 21$

Step 1

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

${(a^{2})}^{2} - 4 a^{2} - 21$

Step 2

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

$u^{2} - 4 u - 21$

Step 3

Factor $u^{2} - 4 u - 21$ using the AC method.

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 $- 21$ and whose sum is $- 4$ .

$- 7, 3$

Write the factored form using these integers.

$(u - 7) (u + 3)$

Step 4

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

$(a^{2} - 7) (a^{2} + 3)$

Factor a^4-4a^2-21

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