Question

I need help once again.

Answer 1

The dimensions of the prism can be 2x, 2x+3 and x+6.

We first factor out the GCF of the trinomial.  The GCF of the coefficients is 2.  Each term has an x in common as well, so the GCF is 2x.

Factoring out the 2x, we have
2x(2x²+15x+18).

To factor the remaining trinomial, we find factors of 2*18=36 that sum to 15.  12*3 = 36 and 12+3 = 15.  We split up 15x into 12x and 3x:

2x(2x²+12x+3x+18)

Now we group together the first two terms in parentheses and the last two:
2x((2x²+12x)+(3x+18))

Factor out the GCF of the first group:
2x(2x(x+6)+(3x+18))

Factor out the GCF of the second group:
2x(2x(x+6)+3(x+6))

Factoring out what these have in common,
2x(x+6)(2x+3)