Answer: [tex](x-2)(2x-3)[/tex]
Explanation:
[tex]2x^2-3x-4x+6[/tex]
I'll group it in a way that I can get common factor numbers.
I can see that 2 and 4 are factorable by 2 and 3 and 6 by 3
[tex](2x^2-4x)+(-3x+6)[/tex]
What do these have in common? 2 and 4 have a 2 in common and they also share an x.
[tex]2x(x-2)[/tex]
Now, what does 3 and 6 have in common? a three. However, we don't usually let our x's be negative, so in order to keep it positive, extract a -3 instead of 3
so, -3/-3 = 1
6/-3=-2
Leaving...
[tex]-3(x-2)[/tex]
Now, put all together.
[tex]2x(x-2)-3(x-2)[/tex]
Look, what do they have in common? Exactly, both have [tex](x-2)[/tex], simply add the terms outside the parentheses and use the same parentheses.
[tex](2x-3)(x-2)[/tex]
If you don't understand why I did this, let x-2 = y
So, you have...
[tex]2xy-3y[/tex]
Factor that y.
[tex]y(2x-3)[/tex]
Replace y with our original value.
[tex](x-2)(2x-3)[/tex]
Same result.
