Could someone explain to me as simply as possible how to factorise

2x^2 + x - 3

I know the answer is (2x + 3) (x - 1) from my textbook but I don't understand the method used.

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- Jan 8th 2011, 10:47 AMNatasha1Factorising a quadratic
Could someone explain to me as simply as possible how to factorise

2x^2 + x - 3

I know the answer is (2x + 3) (x - 1) from my textbook but I don't understand the method used. - Jan 8th 2011, 10:51 AMsnowtea
- Jan 8th 2011, 10:53 AMNatasha1
I saw on the net a method called the AC method but that is also confusing

- Jan 8th 2011, 10:55 AMArchie Meade
It comes from an understanding that

$\displaystyle (2x+a)(x+b)=2x(x+b)+a(x+b)=2x^2+2xb+ax+ab=2x^2+(a+ 2b)x+ab$

so you are looking for the factors of $\displaystyle -3$ for which one of them plus twice the other sum to 1.

They will be 3 and twice $\displaystyle -1.$ - Jan 8th 2011, 10:56 AMAlso sprach Zarathustra
- Jan 8th 2011, 10:58 AMWilmer
Nawwww....I say if not apparent, use the quadratic formula...but that's me!

- Jan 8th 2011, 10:59 AMdwsmith
$\displaystyle (\pm\alpha x\pm\beta)(\pm\lambda x\pm\phi)$

$\displaystyle \beta*\phi=-3\Rightarrow 3*1=3$ Now need to figure out which one is negative.

$\displaystyle \alpha*\lambda=2\Rightarrow 2*1=2$

$\displaystyle \alpha*\phi+\beta*\lambda=1$

Now you need to decide if 3 is beta and 1 is phi, is alpha 1 or 2 and is lambda 1 or 2? - Jan 8th 2011, 11:02 AMTheCoffeeMachine
- Jan 8th 2011, 11:10 AMTheCoffeeMachine
Isn't this just the problem from this thread with just the letter $\displaystyle w$ replaced with $\displaystyle x$?

- Jan 8th 2011, 11:12 AMNatasha1
that is freaky! They are the same but it's pure coincidence. I promise

- Jan 8th 2011, 12:30 PMArchie Meade
- Jan 8th 2011, 04:45 PMWilmer
Compliments will get you everywhere, Archie !