Question

wo 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. (10 points)

Answer 1

Well, to began I suggest factoring out the expression on your own, correctly, to find the mistake they made.
I use to series of blanks to do this as follows:
6x^2-3x-9
3(2x^2-x-3)
i)
__ * __ =-3
(2)__ + __= -1
ii)
1 * -3= -3
(2)1 + -3 = -1
3(2x-3)(x+1)=0

From this form we can derive the x values as 3/2, and -1 if we needed to do so

Explanation:
Although these expressions are equivilant, Jamal's function is more coherent. He expresses that x+1=0 which can be solved as x=-1 rather than having to do 3x+3=0 => 3x=-3 => x=-1. Jamal's factor gives the function within a single step.
This form is the simplest form possible as Jamal noticed that the trinomial was divisible by 3 initially. Jennifer on the other hand did not factor out the 3 initially in the equation. As a result, here function less coherently states the properties of the function.

Hope this helps.