What is 4x^3 + 8x^2 - 96x in factored form

Luckily, you can factor out 4x:

4x^3 + 8x^2 - 96x
=4x(x^2 + 2x - 24)
look easier now?
=4x(x-6)(x+4)

4x(x+6)(x-4)

write the equation of the line in point -slope form that passes through (1,4)and has a slope of 1 over 4

To factor the given expression, we can first look for any common factors that can be factored out. In this case, the expression has a common factor of 4x, so we can factor that out:

4x(x^2 + 2x - 24)

Next, we need to factor the quadratic expression inside the parentheses (x^2 + 2x - 24). To do this, we need to find two numbers whose product is -24 and whose sum is 2.

The factors of -24 are:
-1 and 24
-2 and 12
-3 and 8
-4 and 6

From these pairs, we can see that -4 and 6 have a sum of 2. Hence, we can rewrite the expression as:

4x(x - 4)(x + 6)

Thus, the factored form of the given expression is 4x(x - 4)(x + 6).