i) Factorise x^2 – 7x + 12 ii) Solve x^2 – 7x + 12

i)STEP 1: Make 2 brackets and put an x in each one: (x )(x )
STEP 2: Find 2 numbers when multiplied together make 12 and when added together they make -7
Multiples of 12:
1 x 12 --> 1+12=13 2 x 6 --> 2+6=8 3 x 4 --> 3+4=7-1 x -12 --> -1 + -12 = -13-2 x -6 --> -2 + -6 = -8-3 x -4 --> -3 + -4 = -7
From this, we can see the appropriate multiples would be -3 and -4.
STEP 3: Put -3 and -4 into the brackets now --> (x - 3)(x - 4)
ii)STEP 1: Make the factorised quadratic equal to 0
(x - 3)(x - 4) = 0
STEP 2: Understand that anything multiplied by 0 will always equal to 0
So for (x - 3)(x - 4) to equal 0, (x - 3) = 0 and/or (x - 4) = 0
STEP 3: Solve each bracket
(x - 3) = 0 --> 3 -3 = 0 therefore x = 3(x - 4) = 0 --> 4 - 4 = 0 therefore x = 4
Therefore, solving x² -7x +12 --> x = 3, 4