Question

Factor x2 - 18x + 81. Show your work

Answer 1

To factorise it start with putting the xs in brackets.
(x )(x )
Then you must find 2 numbers which multiply to +81 and sum to -18.
81 is the product of 9×9 or -9×-9.
9+9=+18
-9+-9=-18
So they two numbers must be -9.
So factorised it is (x-9)(x-9) or (x-9)^2

Answer 2

(x - 9)^2

Whenever dealing with a problem like this the first thing you should consider is a square in the last term. Factoring trinomials is always a guess and check procedure, but there are multiple tips to enhance and quicken your guessing. When the last term is a positive square, find the square root of it and double it. Chances are, that result will be the middle term. It is only a matter of addition of subtraction now. If the middle term is negative then it is a subtraction, and if the middle term is positive then vice versa.

81 is a positive square and the square root is 9. By doubling it you get 18. The middle term is negative, so the binomial squared is (x - 9). Hope this helps!