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