HelloGoodbye
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Can someone please explain these solutions please? I'm so confused!

1. 6x2-22x-8

I got the answer as (6x+2)(x-4) but the answer is actually 2(3x+1)(x-4)
why do I need to take the 2 out when I can factorise it already?

2. -4x2+7

I worked it out as (2x-\sqrt 7)(2x+\sqrt 7 but the solution says -(2x-\sqrt 7)(2x+\sqrt 7. I already multiplied by -1 at the start to get rid of -4x so why do I have to multiply by -1 again?
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(Original post by HelloGoodbye)
Can someone please explain these solutions please? I'm so confused!

1. 6x2-22x-8

I got the answer as (6x+2)(x-4) but the answer is actually 2(3x+1)(x-4)
why do I need to take the 2 out when I can factorise it already?

2. -x4x2+7

I worked it out as (2x-\sqrt 7)(2x+\sqrt 7 but the solution says -(2x-\sqrt 7)(2x+\sqrt 7. I already multiplied by -1 at the start to get rid of -4x so why do I have to multiply by -1 again?
(6x+2)(x-4) is factorised but not fully factorised. Since 6x+2 = 2(3x+1) you can factorise further. If a question tells you to factorise, it wants you to factorise fully.

2. If you multiply by -1, it changes the expression i.e. -x^4+7 is different to x^4-7 and if you factorise both you will get different answers,

You're probably getting confused with equations where you can multiply by a constant and get away with it e.g. x^4-7=0 is the same as -x^4+7=0
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VioletPhillippo
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(Original post by HelloGoodbye)
Can someone please explain these solutions please? I'm so confused!

1. 6x2-22x-8

I got the answer as (6x+2)(x-4) but the answer is actually 2(3x+1)(x-4)
why do I need to take the 2 out when I can factorise it already?

2. -4x2+7

I worked it out as (2x-\sqrt 7)(2x+\sqrt 7 but the solution says -(2x-\sqrt 7)(2x+\sqrt 7. I already multiplied by -1 at the start to get rid of -4x so why do I have to multiply by -1 again?
Hiya,
For the first question, you have got the correct answer but they've fully factorised it by pulling out another factor of 6 & 4 which is 2.

For the 2nd question you need to multiply it by -1 to get the -4x². In your answer you have 2x X 2x which is 4x² not -4x² so it must be x by -1 to make it correct. Also I think for the √ that -√7 x +√7 = -7 so you have to x by -1 to get 7(I'm not sure)
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