+193 Write the polynomial in factored form.
4x^3 + 8x^2 – 96x
6x(x + 4)(x – 4)
4x(x – 4)(x + 6)
4x(x + 6)(x + 4)
–4x(x + 6)(x + 4)
Factor the following:
4 x^3 + 8 x^2 - 96 x
Factor 4 x out of 4 x^3 + 8 x^2 - 96 x:
4 x (x^2 + 2 x - 24)
The factors of -24 that sum to 2 are 6 and -4. So, x^2 + 2 x - 24 = (x + 6) (x - 4):
4x (x + 6) (x - 4)
+9519 First, we see the g.c.d of the terms is 4x. We factor this out:
\(4x^3+8x^2-96x = 4x(x^2+2x-24)\).
Then we factor the quadratic. (If you don't know how, you can try expanding the expression in each option.)
\(4x^3+8x^2-96x = 4x(x^2+2x-24)=4x(x+6)(x-4)\).
So we see the answer is the second option.
