Factor 6x^9n-30x^5n-300xn

$6 x^{9} n - 30 x^{5} n - 300 x n$

Step 1

Factor $6 x n$ out of $6 x^{9} n - 30 x^{5} n - 300 x n$ .

Factor $6 x n$ out of $6 x^{9} n$ .

$6 x n (x^{8}) - 30 x^{5} n - 300 x n$

Factor $6 x n$ out of $- 30 x^{5} n$ .

$6 x n (x^{8}) + 6 x n (- 5 x^{4}) - 300 x n$

Factor $6 x n$ out of $- 300 x n$ .

$6 x n (x^{8}) + 6 x n (- 5 x^{4}) + 6 x n (- 50)$

Factor $6 x n$ out of $6 x n (x^{8}) + 6 x n (- 5 x^{4})$ .

$6 x n (x^{8} - 5 x^{4}) + 6 x n (- 50)$

Factor $6 x n$ out of $6 x n (x^{8} - 5 x^{4}) + 6 x n (- 50)$ .

$6 x n (x^{8} - 5 x^{4} - 50)$

Step 2

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$6 x n ({(x^{4})}^{2} - 5 x^{4} - 50)$

Step 3

Let $u = x^{4}$ . Substitute $u$ for all occurrences of $x^{4}$ .

$6 x n (u^{2} - 5 u - 50)$

Step 4

Factor $u^{2} - 5 u - 50$ 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 $- 50$ and whose sum is $- 5$ .

$- 10, 5$

Write the factored form using these integers.

$6 x n ((u - 10) (u + 5))$

Step 5

Factor.

Replace all occurrences of $u$ with $x^{4}$ .

$6 x n ((x^{4} - 10) (x^{4} + 5))$

Remove unnecessary parentheses.

$6 x n (x^{4} - 10) (x^{4} + 5)$

Factor 6x^9n-30x^5n-300xn

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