Jun Cert maths Q from 07 Higher

JuliusCaesar

Need urgent help from a maths genius!

Junior Cert. Maths (Higher) 2007: Paper 1 Question 03

question 3 b (i)

www.e-xamit.ie gives the answer. But I can't work it out at all!

How did 2x squared + 4x -30 become (2x +10) (x-3)? Can anyone help?:(

alan4cult

Right,

2x^2 + 4x - 30

---

x - 3

There are two parts to this
The top of the fraction is a quadratic equation. We need to factorise this.

So 2x^2 + 4x - 30 becomes (2x + 10)(x - 3)

So now it looks like

(2x + 10)(x - 3)

---

(x - 3)

You cancel the (x - 3) from the top and from the bottom
So:

2x + 10 remains

The number 2 is a factor of both 2x and 10 so it becomes

2(x + 5)

johnculloty

JuliusCaesar wrote: »

Need urgent help from a maths genius!

Junior Cert. Maths (Higher) 2007: Paper 1 Question 03

question 3 b (i)

www.e-xamit.ie gives the answer. But I can't work it out at all!

How did 2x squared + 4x -30 become (2x +10) (x-3)? Can anyone help?:(

its easy kido! firstly u put in da 2x and da x in the brackets. then go for factors of 30, 10 and 3! put them in, in such a way that they multiply by the 2x and the x that u get 4x! 10x-6x=4x

lauratkd

johnculloty wrote: »

its easy kido! firstly u put in da 2x and da x in the brackets.

Not always the case with quadratics that have a coefficient on the x^2. A lot of teachers don't really teach this properly and I have come across honours 5th year students who don't understand why if it's 6x^2 you don't automatically just put 6x and x in the brackets... Very frustrating to have to teach this again at that stage.

JuliusCaesar

still don't ubderstand.

What happened 4x?

QUOTE: The top of the fraction is a quadratic equation. We need to factorise this.

So 2x^2 + 4x - 30 becomes (2x + 10)(x - 3)UNQUOTE

i cansee that 3 X 10 = 30, but what happened the rest? (and when in real life would you ever need this? maybe I should do Applied maths...if it means what I think it might mean. )totally confused here.

but thanks maths geniuses.

PurpleFistMixer

Hm. Explaining how to factorise is tricky, it's a bit of a weird idea.
I'll try a simpler example.

To factorise, say, x^2 +5x + 6 = 0
As the coefficient of x^2 is 1, that is, it's just x^2, you'll just have your brackets like this...
(x )(x )
What you'll put in the rest comes now...
You can only put in the factors of six.
Factors of six are 2 and 3, or 6 and 1.
The question is now which of those sum to 5? 2 + 3 of course.
So you stick those in, and your brackets look like this:
(x + 2)(x + 3)

Factorising quadratic equations is extremely useful, you need it a lot... in most parts of maths to be honest. One example from applied maths is the following: (probably shoudln't read this unless you want to get confused )
The equation to find the distance (s) travelled by a particle moving at initial speed (u) with acceleration (a) for t seconds is:
s = ut + 1/2a(t^2), which, if you rewrite the other variables as random numbers, comes out looking like this
t^2 + 4t - 5 = 0 (i just made the 5 and the 2 up for the sake of simplicity), so to find the t, you'll need to factorise the equation. (And in this case it would turn out as (t + 5)(t - 1) )

But enough of that. The example you have here,
2x^2 + 4x - 30

Okay, we have 2x^2, so the brackets will be like this:
(2x )(x )
(if we had 3x^2 one would be 3x and the other x, if we had 4x^2 it could be either 2x in both of the brackets of 4x in one and 1x in the other ,you have to put the factors of it in, if you get me!)
Next question: What are the factors of -30? -1 and 30, 1 and -30, -2 and 15, 2 and -15, -3 and 10, 3 and -10, -5 and 6, 5 and -6
Now, normally you'll go "which of these sum to 4?" but, because we have a 2x in one of our brackets, one of the factors will be multiplied by two, so it's a little harder. You can work it out by trial and error basically (ie, does 1x2 and -30 sum to 4? no, does 2x2 and -15 sum to 4? no, does 3x2 and -10 sum to 4? No, but -3x2 + 10 = 4)
So our factors are -3 and 10
The question is now, which bracket do you put each one in?
The rule is, you put the one you want multiplied by the 2 in the OTHER bracket, so we have...
(2x + 10)(x - 3)

And one is done. I hope that made SOME sense. I advise asking your teacher, it's easier to explain things using a blackboard and.. well, teachers explain a lot better than I do.

alan4cult

JuliusCaesar wrote: »

still don't ubderstand.

What happened 4x?

QUOTE: The top of the fraction is a quadratic equation. We need to factorise this.

So 2x^2 + 4x - 30 becomes (2x + 10)(x - 3)UNQUOTE

i cansee that 3 X 10 = 30, but what happened the rest? (and when in real life would you ever need this? maybe I should do Applied maths...if it means what I think it might mean. )totally confused here.

but thanks maths geniuses.

So what happens the 4x?
Watch:

The equation is 2x^2 + 4x - 30
We have factorised it and it has now become (2x + 10)(x - 3)

Now remember one of the first things you did in algebra was to expand brackets?
Lets expand:
(2x + 10)(x - 3)
= 2x(x - 3) + 10(x - 3)
= 2x^2 - 6x + 10x - 30
= 2x^2 + 4x - 30

Hey look our 4x came back to join us!
It was simply disguised in -6x + 10x.