Question

What is the factored form of 6n4 – 24n3 + 18n?

Answer 1

6n(n - 1)(n^2 - 3n - 3).

Explanation:

The GCF = 6n.

6n^4 - 24n^3 + 18n

= 6n(n^3 - 4n^2 + 3)

Putting n = 1 in the expression in the parentheses:

(1)^3 - 4(1)^2 + 3 = 0 so n - 1 is a factor.

Dividing:

n - 1 ) n^3 - 4n^2 + 0n + 3 ( n^2 - 3n - 3

n^3 - n^2

-3n^2 + 0n

-3n62 + 3n

- 3n + 3

-3n + 3

So the factors are 6n(n - 1)(n^2 - 3n - 3).