Write the polynomial in factored form. 4x3+8x2−96x (1 point) Responses 4x(x−4)(x+6) 4 x open paren x minus 4 close paren open paren x plus 6 close paren −4x(x+6)(x+4) negative 4 x open paren x plus 6 close paren open paren x plus 4 close paren 6x(x+4)(x−4) 6 x open paren x plus 4 close paren open paren x minus 4 close paren 4x(x+6)(x+4)
To factor the polynomial 4x^3 + 8x^2 - 96x, we first look for common factors in each term:
The common factor here is 4x, so we factor that out first:
4x(x^2 + 2x - 24)
Now, we need to factor the quadratic equation inside the parentheses. To do that, we look for two numbers that multiply to -24 (since it's the product of the last term) and add up to 2 (since it's the coefficient of the middle term):
The numbers that satisfy this are 6 and -4, since 6 * -4 = -24 and 6 + (-4) = 2.
So, we factor the quadratic part as:
x^2 + 2x - 24 = (x - 4)(x + 6)
Putting it all back together with the factored out 4x, we get:
4x(x - 4)(x + 6)
The correct answer is 4x(x - 4)(x + 6).