I'll assume your original quadratic should read x^2 - 9x + 20 = 0.
When you have a quadratic with leading coefficient equal to 1, and integer coefficients, there is a simple process to follow to check whether the polynomial will or will not factor with integer constants.
Step 1: Write down all pairs of integers with product equal to the constant term.
Step 2: Look in your list for a pair whose SUM equals the middle coefficient. These are the appropriate choices. (IF there is no such pair, the given quadratic won't factor this way)
For yours, the constant is 20. There are two possible choices: 4 \text{ and } 5 and -4 \text{ and } -5. Since the second pair sum to -9, these are the choices, and you know
<br />
x^2 - 9x + 20 = (x-4)(x-5)<br />
As another example, consider factoring
<br />
x^2 - 6x - 27 = 0<br />
Step 1: Look for integer pairs that multipy to -27. There are two choices: 3 \text{ and } -9, and -3 \text{ and } 9. The first pair has sum -6, so those are your choices.
<br />
x^2 - 6x- 27 = 0 \Rightarrow (x-9)(x+3) = 0<br />
so the solutions are x = 9 \text{ and } x = -3.
Finally, consider x^2 - 11x + 8 = 0. Sets of integers with a product of 8 are 1 \text{ and } 8, 2 \text{ and } 4, -1 \text{ and } -8, -2 \text{ and } -4. None of these pairs sum to -11, so this polynomial doesn't factor using integers.
It is very important to remember that this method works ONLY when the leading coefficient (the coefficient of x^2) equals 1.