Factor Completely
2x^3-40x^2-192x
I have a common factor of x so I rewrote the problem as
x(x^2-40x+192) then trying to use FOIL rewrote as
(x ) (x )
And that is where i'm stuck.
The last one shold be
(x ) (x )
You factored out the 2x incorrectly. You should end up with 2x(x^2-20x+96).
The expression in parentheses can be factored into
(x-12)(x-8).
Now put it all together.
AAAAAAAAAAAAAAAHHHHHHH...thanks..it's in the details.
To factor the expression completely, we can proceed as follows:
1. Start with the expression: 2x^3 - 40x^2 - 192x.
2. First, look for any common factors among all the terms. In this case, there is a common factor of 2x, so we can rewrite the expression as: 2x(x^2 - 20x - 96).
3. Now, let's focus on factoring the quadratic term inside the parentheses: x^2 - 20x - 96.
4. We can try factoring this quadratic by looking for two numbers that multiply to -96 (the coefficient of the constant term), and add up to -20 (the coefficient of the linear term). The numbers that satisfy this condition are -24 and 4.
5. Rewrite the linear term (-20x) using -24x and 4x. Now we have: x^2 - 24x + 4x - 96.
6. Group the terms together: (x^2 - 24x) + (4x - 96).
7. Factor out the Greatest Common Factor (GCF) from each group: x(x - 24) + 4(x - 24).
8. Notice that we now have a common binomial factor of (x - 24). Factor it out: (x - 24)(x + 4).
9. Putting it all together, the completely factored expression is: 2x(x - 24)(x + 4).
So, the expression 2x^3 - 40x^2 - 192x factors completely as 2x(x - 24)(x + 4).