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

1 Answer

4 votes

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.

User Tgeng
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