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

anonymous · Answer

both the students are right

anonymous · Answer

but only difference is that one take 3 out from the factor so both are correct

mathmate · Answer

Both students factored correctly, but one did not factor completely.

anonymous · Answer

and its not a trinomial its a polynomial

mathmate · Answer

@ambujverma 
Monomials, binomials and trinomials are all polynomials.

anonymous · Answer

yaaaaaaaaaaaaa

hayhayz · Answer

so jamal did not factor it completely right

anonymous · Answer

jamal did it right

hayhayz · Answer

Can you explain why/how the student did not factor completely?

mathmate · Answer

Jennifer's factor:
(2x-3)(3x+3)
Notice that the second factor contains a common factor of 3, therefore it can be factored as (3x+3)=3(x+1), or the complete factor would be
(2x-3) (3)(x+1), or
3(2x-3)(x+1)
That's why Jennifer did not factor completely because she missed the common factor 3.

In fact, whenever trying to factor, we look for common factor for ALL the terms and factor that out as a FIRST step.  This will make the remaining factoring much easier.

For example, 
factor 512x^2+1024x-1536.
We first take out the common factor 512 to reduce the expression to
512(x^2+2x-3)
which can be easily factored into
512(x+3)(x-1)

hayhayz · Answer

@mathmate thank you so much!

mathmate · Answer

You're welcome!   :)