Factor completely by factoring out any common factors and then factoring by grouping.
6x2 – 5xy + 6x – 5y

Question

Factor completely by factoring out any common factors and then factoring by grouping.
6x2 – 5xy + 6x – 5y

mathstudent55 · Answer

1. Is there a common factor in all 4 terms?

anonymous · Answer

not that I see at all. shouldn't I just continue to factor?

mathstudent55 · Answer

Good.
2. Is there a common factor you can take out of the first two terms?
Is there a factor you can factor out of the last two terms?

mathstudent55 · Answer

Can you factor a common factor out of
$6x^2 - 5xy$

Can you factor a common factor out of 
$6x - 5y$

anonymous · Answer

I can take x out of the first but nothing from the second set of terms

mathstudent55 · Answer

You are correct, but here's the trick.
In factoring a 4-term polynomial by grouping, you always need to factor something out even if that thing is simply 1.

$6x^2 - 5xy + 6x - 5y$

$= x(6x - 5y) + 1(6x - 5y) $

Ok?

anonymous · Answer

ooooooooh ok, thank you

mathstudent55 · Answer

3. Now you do the final step.
Factor out the common factor of 6x - 5.

$= x(6x - 5y) + 1(6x - 5y)$

$ (6x - 5y)(x + 1) $