How to solve polynomial by factoring and using the zero product principle for x^3+3x^2=4x+12

The solutions to the equation are - 3,-2,2

Step-by-step explanation:

x^3+3x^2=4x+12

Subtract 4x + 12 from each side

x^3+3x^2-4x-12=4x+12-4x-12

x^3+3x^2-4x-12=0

I will use factoring by grouping

x^3+3x^2 - 4x-12=0

I will factor out x^2 from the first group and - 4 from the second group

x^2 (x+3) - 4 (x+3) = 0

Now we can factor out (x+3)

(x+3) (x^2-4) = 0

We can use the zero product principle since the right hand side is equal to 0

x+3 = 0 x^2-4 = 0

x+3-3=0-3 x^2 - 4+4=0+4

x=-3 x^2=4

Take the square root of each side

sqrt (x^2) = sqrt (4)

x=±2

The solutions to the equation are - 3,-2,2