Two students, Jennifer and Jamal, factored the trinomial 6x2 − 3x − 9. Jamal factored it as 3(2x − 3)(x + 1) and Jennifer factored it as (2x − 3)(3x + 3). Indicate which student factored the trinomial completely and which student did not, and explain why.

Question

Zepdrix · Answer

Factoring a 3 out of each term gives us,
$\large\rm 3(2x^2-x-3)$

2 on the leading term, multiply it by the -3 to get -6.
So our middle term needs to be broken down into the factors of -6 which add to -1. We'll rewrite -x as 2x-3x.

$\large\rm 3(2x^2+2x-3x-3)$

Continue by factoring by grouping,

$\large\rm 3\left[(2x^2+2x)+(-3x-3)\right]$

Pulling 2x out of the first set,
$\large\rm 3\left[2x(x+1)+(-3x-3)\right]$

and -3 out of the other,
$\large\rm 3\left[2x(x+1)-3(x+1)\right]$

Then finish up by factoring (x+1) out of each term,
$\large\rm 3(x+1)(2x-3)$

Zepdrix · Answer

Jennifer needs to factor a 3 out of her last term.