Answer:
(x - 6)(x - 3)
Explanation:
r^2 - 9r + 18
Replace "r" with "x" (optional).
x^2 - 9x + 18
In the form of "ax^2 + bx + c", you first multiply a and c, in this case 1*18 = 18. Next, you split 18 into two factors of 18 that produces 18 when multiplied together, like -1 and -18, 2 and 9, -3 and -6 (yes they can be negative! As long as they multiplies to a*c, they are fine). Then, you try to find a pair of factors that add up to "bx", in this case "-9x". In other words, you try to find a pair of factors that can replace "-9x" in the expression without changing the expression. In this case, you can use "-3" and "-6", they add up to "-9", they also multiplies to "18".
Most of the times, you can just do the steps above in your head.
Now, with the pair that we found, we can substitute the two numbers in for "bx" or "-9x".
x^2 -3x -6x + 18
Notice that the expression did not change, just written in a different way.
Now group the first two terms and the last two terms together.
(x^2 - 3x) + (-6x + 18)
Factor out what ever you can factor.
x(x - 3) + (-6)(x - 3) (We try to keep the "x" positive)
Now notice we have two "(x - 3)" in the form of ab + cb with b=(x - 3).
We can group the "(x - 3)" together. AKA ab + cb ---> (a + c)b
(x + (-6))(x-3)
(x - 6)(x - 3)
After enough practice, you can do all of these in your head.