Multi-Step: Factoring out and Factoring Completely

Question

The volume of a prism is 6x³⁺14x²+4x cm³. Find the dimensions of the prism:

     a. Factor out common terms.

     b. Factor completely to find the dimensions.

Answer 1

6x³ + 14x² + 4x = 2x(3x² + 7x + 2)

 

                             = 2x(3x + 1)(x + 2)

Answer 2

First, let’s factor the expression 6x^3 + 14x^2 +4x
                                2x(3x^2+7x+2)      (factor out 2x)
                                2x(3x+1)(x+2)        (find factors or use quadratic equation)

Now,  for a triangular prism, the volume is (1/2)*b*h*l     [note: area of triangle times length]

So, we have some choices for b, h, and l and we have to use (1/2) on one of the choices.

        One of the possibilities is:
                                    b = 4x
                                    h = 3x+1
                                    l = x+2

Can you think what the other choices might be?

Answer 3

I actually am confused by your question. Can you paraphrase?