Some quadratics have a number in front of the , eg: .
With these kind of questions a slightly modified version of the basic method is needed:
Eg1 multiply the number (2 in this case) by the loose number (15). .
Now find 2 numbers which multiply to give this number (30)
and which also add to give the middle number (13 in this case).
Factors of 30: (1, 30), (2, 15), (3, 10). Use +3 and +10 because 3 + 10 = 13
Split the middle term into these 2 numbers (+3 and +10) but bring down the outside terms
Now factorise the first pair: , and the second pair:
NB. Make sure you have the same thing in each bracket.
Put into 2 brackets.
Eg2 Factors of : (1, 48), (2, 24), (3, 16). Use +3 and +16 because 3 + 16 = 19
Split the middle term into +3 and +16
Factorise in pairs
Put into 2 brackets
Eg3 Factors of 60 which add to -23: Use -8 and -15 because
Factorise in pairs
Put into 2 brackets