Question

A shipping box in the shape of a rectangular prism has a volume of 12x^3+32x^2+20x. What are the possible dimesions of the box?

Answer 1

Anyone who answers please show your work. I want to see how you did it.

Answer 2

PS. It's a binomial or trinomial or something like that.

Answer 3

The first thing you should do is take out any common factors
\[12x^3+32x^2+20x\]\[4x(3x^2+8x+5)\]
Now you need to factor 3x^2+8x+5. To do this you need to find the factors of 'ac' that add up to b. In this case ac=15, and b=8. The factors of 15 that add up to 8 are 5 and 3.
\[3x^2+3x+5x+5\]\[3x(x+1)+5(x+1)\]\[(3x+5)(x+1)\]
So in the end,
\[12x^3+32x^2+20x=4x(3x+5)(x+1)\]
Possible dimension of this box are 4x, 3x+5, and x+1.

Answer 4

Thank you.