When factorising quadratics follow the following steps:
Step 1: Are there any obvious factors that can be factorised out in the normal way?
Eg1 Take 4 out
Eg2 Take out
Eg3 Take out
Eg4
Step 2: Are there only 2 terms? If so, are they a ‘Difference of 2 Squares’?
Step 3: If there are three terms, an , an term and a number term (eg ), then:
(a) look at the number term (6 in this case) and try to find two numbers which multiply to give this number and which also add to give the number with the (the 5 in this case). Do this systematically by going through the pairs of factors in turn.
Factors of 6 are : +1 and +6, but these will NOT add to give 5
+2 and +3, these WILL add to give 5.
(b) put these two numbers into 2 brackets (don’t forget about +/- signs)
Eg1
Eg2 Factors of 24: (1 & 24), (2 & 12), (3 & 8), (4 & 6). Use +4 and +6 because only 4 + 6 = 10
Put +4 and +6 into the brackets
Eg3 Factors of 32: (1, 32), (2, 16), (4, 8). Use +4 and -8 because only 4 – 8 = -4
Put +4 and -8 into the brackets