6x²-13x+6
Multiply the 6 by the 6 ignoring signs. Get 36
Write down all the ways to have two positive integers
which have product 36, starting with 36*1
36*1
18*2
12*3
9*4
6*6
Since the last sign 6x²-13x+6 is +, ADD them,
and place the SUM out beside that:
36*1 36+1=37
18*2 18+2=20
12*3 12+3=15
9*4 9+4=13
6*6 6+6=12
Now, again ignoring signs, we find in that list of
sums the coefficient of the middle term in 6x²-13x+6
So we replace the number 13 by 9+4
6x²-13x+6
6x²-(9+4)x+6
Then we distribute to remove the parentheses:
6x²-9x-4x+6
Factor the first two terms 6x²-9x by taking out the
greatest common factor, 3x, getting 3x(2x-3)
Factor the last two terms -4x+6 by taking out the
greatest common factor, getting -2(2x-3)
So we have
3x(2x-3)-2(2x-3)
Notice that there is a common factor, (2x-3)
3x(2x-3)-2(2x-3)
which we can factor out leaving the 3x and the -2 to put
in parentheses:
(2x-3)(3x-2)
Edwin
