The other tutor suggests the trial and error method.
This is the AC-method:
Factor: 4x²-13x+9
Multiply the 4 by the 9 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 in 4x²-13x+9 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 13, the coefficient of the middle term in 4x²-13x+9
So we replace the number 13 by 9+4
4x²-13x+9
4x²-(9+4)x+9
Then we distribute to remove the parentheses:
4x²-9x-4x+9
Factor the first two terms 4x²-9x by taking out the
greatest common factor, x, getting x(4x-9)
Factor the last two terms -4x+9 by taking out the
greatest common factor, -1, getting -1(4x-9)
So we have
x(4x-9)-1(4x-9)
Notice that there is a common factor, (4x-9)
x(4x-9)-1(4x-9)
which we can factor out leaving the x and the -1 to put
in parentheses:
(4x-9)(x-1)
Edwin
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