This jigsaw will help you revise simplifying expressions, inequalities, expanding brackets and factorisation. Is this the worst joke yet?
In the last exercise you learnt how to factorise quadratic expressions. We will now use this in order to solve simple quadratic equations.
Suppose x²+9x +20 = 0
If we factorise we get (x+4) (x+5) = 0
In other words, two numbers multiply together to make 0. This means one of those numbers must be 0!
So we know EITHER x+4 = 0 OR x+5 = 0
If x +4 = 0 x = -4
If x+5 =0 then x=-5
So the solution is x = -4 or -5
Remember quadratic equations will nearly always have 2 solutions.
To do this look for a pair of numbers that add up to 9 and muliply together to make 20.
If you can’t find the right pair, write down all the pairs of factors of 20.
1 x 20
2 x 10
4 x 5
Now we can see the correct pair is 4 and 5.
So x²+9x +20=(x+4)(x+5)
Check this by multiplying out the brackets.
Lets try one involving negative numbers.
x² -x -12
The pairs of factors of -12 are
-12 x 1
-6 x 2
-4 x 3
-3 x 4
-2 x 6
-1 x 12
The pair that add up to -1 (because there is -x in the expression) are -4 and 3
So x² -x -12=(x-4)(x+3)
If you would rather use pen and paper there is a paper version here. Check your answers using the interactive version.