How do I factorise a quadratic equation?
A quadratic equation is one that takes the form.. ax2 + bx +c = 0
Factorising an equation like this involves putting the equation into two brackets.
The method varies slightly dependent on whether a = 1 or not. Lets go through an example to see what to do!
Take the equation x2 - x - 12 = 0
To factorise the equation we need to find two numbers that multiply to get c and add/subtract to get b.
In this case, -4 and 3 are two numbers that multiply to -12 and add to -1.
Therefore we have two brackets...
(x - 4)(x + 3) = 0
We can check this is correct by expanding the brackets to see if we get the original equation...
x2 - 4x + 3x - 12 = 0
x2 - x - 12 = 0 ... our factorising was correct!
We can then solve the equation to get values for x by making each bracket equal to zero...
(x - 4) = 0 ... x = 4
(x + 3) = 0 ... x = -3
So what if a is not equal to 1...
The first terms in the brackets must multiply to give a. Lets look at an example again!
2x2 - 9x - 5 = 0
The initial brackets would need to be (2x )(x 0) = 0 in order to get 2x2
Now to get c, the only option is 1 x 5 for the second part of the brackets. Therefore we have two options...
(2x 5)(x 1)
or
(2x 1)(x 5)
Take option 1... this multiples to give 2x and 5x which add or subtract to give 3x or 7x
Take option 2... this multiples to give 10x and 1x which add or subtract to give 9x or 11x
Looking back at our equation we are looking for 9x, so option 2 would be the correct option. We just need to put the signs in correctly to get the result...
(2x + 1)(x - 5) = 0
Again we can check by expanding, and can carry on to solve the equation as above.
