8x3 – 12x2 + 6x – 9
This is a polynomial expression.
a little synthetic division yields
8x^3 – 12x^2 + 6x – 9 = (2x-3)(4x^2+3)
or as the difference of two cubes,
(2x-1)^3 - 8 = (2x-1-2)((2x-1)^2 + 2(2x-1) + 4)
These are both correct factorizations of the polynomial expression. Good job!
To simplify the expression 8x3 – 12x2 + 6x – 9, we can combine like terms.
First, let's look for terms with the same variable raised to the same power. In this expression, we have 8x3 and -12x2.
We can add these terms together to get (8x3 - 12x2).
Next, let's look for terms with variable x without any power. In this expression, we have 6x.
Now, let's add this term to our previous result. We have (8x3 - 12x2 + 6x).
Finally, we have a constant term -9.
We can add this constant term to our previous result. The simplified expression is therefore:
8x3 – 12x2 + 6x – 9