A polynomial has been factored below, but some constants are missing.

3x^3+6x^2-24x=ax (x+b) (x+c)

What are the missing values of a, b, and c

a=3, b=4, and c=-2

Step-by-step explanation:

3x^3+6x^2-24x

Each of the three terms has a common factor of 3x.

3x (x^2+2x-8)

Now can you think of two numbers that multiply to be - 8 and add to be 2?

How about 4 and - 2? 4 (-2) = -8 and 4 + (-2) + 2.

So the factored form of x^2+2x-8 is (x+4) (x-2).

We can check this by using foil.

First: x (x) = x^2

Outer: x (-2) = -2x

Inner: 4 (x) = 4x

Last: 4 (-2) = -8

Add them up! This gives you x^2+2x-8 which is the desired result.

So the factored form of 3x^3+6x^2-24x is 3x (x+4) (x-2).

Comparing 3x (x+4) (x-2) to ax (x+b) (x+c) gives us a=3, b=4, and c=-2