Perform the operation(s) and simplify completely.

(8x3−12x2+18x−27)2x−3 − x2+4x

1 answer

First, we will simplify the expression (8x^3 - 12x^2 + 18x - 27) / (2x - 3):

(8x^3 - 12x^2 + 18x - 27) / (2x - 3)
Factor out common terms in the numerator:
[2(4x^3 - 6x^2 + 9x - 13)] / (2x - 3)
Notice that we can factor out a 2 from the numerator as well:

2(4x^3 - 6x^2 + 9x - 13) / (2x - 3)
Now, simplify the expression x^2 + 4x:

x^2 + 4x
Factor out x:
x(x + 4)

Combining the two simplified expressions, we have:

2(4x^3 - 6x^2 + 9x - 13) / (2x - 3) - x(x + 4)