Question

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

Answer 1

6n^4-24n^3+18n
6n(n^3-4n^2+3)
6n(n-1)(n^2-3n-3)

Answer 2

Explanation:

Notice to facts:

• The numbers 6, -4 and 18 have a common factor: 6.
• In all the terms (n⁴, n³, n) are a factor n.

The expression has a common factor 6n. Then,

6n⁴-24n³+18n = 6n(n³-4n²+3).

In order to factor the term n³-4n²+3 we use Ruffini-Horner rule, which gives us that

n³-4n²+3 = (n-1)(n²-3n-3).

Then,

6n⁴-24n³+18n = 6n(n³-4n²+3) = 6n(n-1)(n²-3n-3).

If you don't know the formula for the general solution of second degree equation, you are done. Otherwise, it is only to use it in the quadratic factor.