Finite Math Examples

$3^{2 n} - 3^{n} - 20$

Step 1

Rewrite $3^{2 n}$ as ${(3^{n})}^{2}$ .

${(3^{n})}^{2} - 3^{n} - 20$

Step 2

Let $u = 3^{n}$ . Substitute $u$ for all occurrences of $3^{n}$ .

$u^{2} - u - 20$

Step 3

Factor $u^{2} - u - 20$ 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 $- 1$ .

$- 5, 4$

Step 3.2

Write the factored form using these integers.

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

Step 4

Replace all occurrences of $u$ with $3^{n}$ .

$(3^{n} - 5) (3^{n} + 4)$