Factor completely. 6x^4-9x^3-36x^2+54x

3x (2x - 3) (x^2 - 6)

Step-by-step explanation:

6x^4 - 9x^3 - 36x^2 + 54x =

First, factor out the largest common factor of all terms. It is 3x.

= 3x (2x^3 - 3x^2 - 12x + 18)

Now you have 4 terms inside the parentheses. Try factoring by grouping. Factor a the largest common factor out of the first two terms, and factor the largest common factor out of the last two terms.

= 3x[x^2 (2x - 3) - 6 (2x - 3) ]

Now you have a common term of (2x - 3), so factor that out.

= 3x (2x - 3) (x^2 - 6)

Factoring means factoring completely, so we look at each factor to see if it can be factored further. Let's look at each factor.

3x is not factorable.

2x - 3 is not factorable.

x^2 - 6 is a difference, but since 6 is not a perfect square, it is not a difference of squares, so it cannot be factored.

Answer: 3x (2x - 3) (x^2 - 6)

3x (2x-3) (x2-6)