Question

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.

Answer 1

To factor this:

1st: take out GCF
3(2x^2 - x - 3)

2nd: do AC method by starting with what 2 numbers equal -6 [ac] and add up to be -1 [b]

Two numbers: -3, 2

3rd: split b into these two numbers

3( 2x^2 + 2x - 3x - 3)

4th: group the first two and last two terms and take out their GCF's

3( 2x[ x+ 1 ] -3 [x+1] )

5th: finish up
3( 2x - 3)( x + 1 )

Jamal factored it completely because he took out the GCF in the first step while Jennifer did not.