Stah's Factorising Guide!!

To all of you budding mathematicians out there who need an EASY, QUICK and RELIABE way to factorise quadratic equations...

LOOK NO FURTHER!!!!! IT HAS ARRIVEDD!!!

I struggled in younger years at school with factorising before i took the quadratic equation for what it was worth and developed my own technique through trial and error... This technique i later found was known as GROUP FACTORISING.. Below is a tutorial and homework/exam aid on how to factorise QUICKLY and EASILY using this method.... Hope it helps


------------------------------------------------------------------------

1) What are quadratic equations?

Simply put, quadratic equations are any equation that come in the form OR can be rearranged into the form :

ax(squared)+bx+c

-------------------------------------------------------------------------

2) Where do we use quadratic equations?

Quadratic Equations are fundamental throughout mathematics beyond elementary school level. They are used in engineering work, architecture, accountancy and several other career paths.. As well as the obvious to get through the mathematics exams.

--------------------------------------------------------------------------

3) THE METHOD

This method will make factorising a LOT easier ( if it doesn't then you seriously are screwed ).

When a quadratic equation is COMPLETELY factorised its end result is 2 sets of closed brackets I.E:

(2x+2)(x+4)

This method will show you how to get to this complete stage from the quadratic equation stage.

STEP 1 -

ax(squared) + bx + c

Multiply a by c and write down the value you get on a piece of paper ( one practised this will no longer be necessary).

For the value you get find all of its pairs of factors ( two numbers which multiply to give the value ) and write them down beneath the value.

I.E. x(squared)+4x+3 a=1 , b=4 , c=3
a x c = 3

List of factors

3 1
-3 -1

From the list of factors select the pair which plus together to give the value 'b'

I . E . 3+1 = 4 WHEREAS -3 + (-1) = -4

so the correct pair are 3 and 1



replace bx with these two numbers multiplied by x.

I.E x(squared)+(1)x+3x+3

You now have four values in the equation. Split these up into two sets of values.

I.E x(squared)+x 3x+3

Now take what is common in both of these sets out of them

I.E x(x+1) 3(x+1)

NOTE HOW BOTH BRACKETS HAVE THE SAME QUANTITY! THEY SHOULD ALWAYS HAVE THE SAME QUANTITY!

Now form another bracket from the two entities outside of the brackets

I.E (x+3)

You can treat both brackets with the same values inside as 1 now and thus complete the equation.

I.E (x+1)(x+3)


TRADADA!!!!

factorising made easy(er).

Hope that helped! If it did/didn't then don't be shy and speak up