When you factor by grouping, should the binomials match up in the second to last step?

Question

In problems like 2x^2+3n-9 I keep getting x(x+6)-3(x-3) but don't know if its right or where to go from there

Answer 1

1) Given: 2x^2+3x-9

2) Our coefficients a*c = 2*-9 = -18

3) The factors that make up -18 must add up to our b coefficient.

4) If we factor -18 out, our options are (18,1),(2,9),(3,6) (Ahah!! it must be (3,6).  But, it was -18, right? So one of those values must be negative too.  To get to positive 3 in our polynomial, our option must be (-3,6)

5)So now we have to think about this.  We have 2x^2 + 6x - 3x - 9

6) Now, we can group them! (2x^2 + 6x) + (-3x - 9)

7) Factor out the common terms. 2x(x+3) -3(x+3)  Voila!!

8) (2x-3)(x+3) is our final answer here.  This last step is the tricky part.