Answer:
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
