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