Factor the expression.
120k^3-80k^2+144k-96
why stop there?
8(3k-2)(5k^2+6)
We can start by factoring out the greatest common factor, which is 8:
8(15k^3 - 10k^2 + 18k - 12)
Now, we can group terms and factor by grouping:
8(15k^3 - 10k^2 + 18k - 12)
= 8(15k^3 + 18k - 10k^2 - 12)
Next, we can factor out the common factors from the two pairs of terms:
8(k^2(15k + 18) - 2(5k^2 + 6))
Finally, we can factor out the common factor of 2 from each term in the parentheses:
8(k^2(15k + 18) - 2(5k^2 + 6))
= 8(k^2(15k + 18) - 2(2)(5k^2 + 3))
Thus, the fully factored expression is:
8(k^2(15k + 18) - 4(5k^2 + 3))