Hey!! So to factor it, you want to see what 2 numbers will multiply and make 9 and what 2 numbers will add and make -6. so 9 and 1 and -9 and -1 make 9 but they dont make -6. 3 and 3 and -3 and -3 make 9, but we need to see which one makes -6. that would be -3 and -3 so the answer is (x-3)(x-3)
you can foil to make sure. x * x is x^2 -3*x=-3x -3*x=-3x -3x-3x = -6x -3*-3 is 9 so it is x^2-6x+9 which makes the original equation
If you need help factoring, you should talk to your teacher, but here's how I do it:
1. Look at the first term and its coefficient. Think of two possible numbers that would multiply to get the first term (i.e. 3x and 2x for 6x²) and put them first in the parentheses. You can also write all possible combinations on the side. However, this time, the only combination would be x and x multiplying to get x².
(x )(x )
2. Next, look at the last term. What two numbers multiply to get 9? Remember that two negative numbers can multiply to produce a positive one too. Basically, you're looking for two numbers that multiply to get 9 and add together to get -6. You might try all of the possible combinations, but none will work. In that case, you would go back to step 1 and try a different first term. In this case, though, there's only one combination for the first places, so that won't be necessary.
Only two numbers less than 100 have a factor of 40: 40 (1 x 40) and 80 (2 x 40). Since 40 is a factor of both 40 and 80, 10 must also be a factor - indeed, 40 = 4 x 10 and 80 = 8 x 10.
