Question

what is the factor of
2x^2+2x-4

Answer 1

Can you see a common factor in each of the terms there?

Answer 2

2 :)

Answer 3

Ok, so factorise 2 from the equation to outside a pair of brackets.

Answer 4

(2x )(x )?

Answer 5

Think of it as 2(x^2+x-2). Do you see what i mean?

Answer 6

oh yes.

Answer 7

Right. Are you aware of the Product Sum Factor method of factorisation?

Answer 8

no.

Answer 9

Ok, well think of the equation you gave me as ax^2 + bx + c. Where a in this case is 1, b is 1 and c is -2.

Answer 10

What you are looking for, is two numbers that multiply together to give c and add together to give b. In this case: what x what gives -2 and when added together gives 1.

Answer 11

+2
-1

Answer 12

Right! Good Job! So now think of it as (x+2)(x-1) ok? Thats the product sum factor method, which does not work all the time. Put the two things we have done together and you get?

Answer 13

2x^2+1x-2?

Answer 14

wait

Answer 15

Take it back a step. Remember how we took the two outside the brackets. And then we factorised what was in the brackets.

Answer 16

x^2 +1x +2

Answer 17

Take it back a step. Remember how we had 2(x^2+x-2)?

Answer 18

Just then using PSF we factorised x^2+x-2

Answer 19

And we got (x+2)(x-1). Right?

Answer 20

yeah

Answer 21

So (x+2)(x-1) and x^2+x-2 are basically the same thing right? Because we just factorised.

Answer 22

oh wait

Answer 23

ahhhhhhhhhhhhh :)

Answer 24

So whats the answer you get?

Answer 25

wait wait where did the 2go?

Answer 26

Thats what I am getting at. Ok ill try to put it more simply. If we let x^2+x-2 equal a pronumeral, say y. And since we had the 2 outside it, its really 2y. And we just said before, that y could also be (x+2)(x-1) didnt we? So sub in that second value of y. And you get?

Answer 27

i dont really get it. Sorry.

Answer 28

Im trying to think of a simple way to do this. (x+2)(x-1) is = x^2 +x - 2 right?

Answer 29

If and when you come back to this. The answer is 2(x+2)(x-1) think about what I said and see if you can make sense of it.