Question

Factor: 2x^2 - 3x - 4x + 6
oh my god help me

Answer 1

Answer:
`(x-2)(2x-3)`

Step-by-step explanation:

`2x^2-3x-4x+6`

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

`(2x^2-4x)+(-3x+6)`

What do these have in common? 2 and 4 have a 2 in common and they also share an x.

`2x(x-2)`

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...

`-3(x-2)`

Now, put all together.

`2x(x-2)-3(x-2)`

Look, what do they have in common? Exactly, both have
`(x-2)`, simply add the terms outside the parentheses and use the same parentheses.

`(2x-3)(x-2)`

If you don't understand why I did this, let x-2 = y

So, you have...

`2xy-3y`

Factor that y.

`y(2x-3)`

Replace y with our original value.

`(x-2)(2x-3)`

Same result.