Can someone please help me with the following?:
Factor each expression completely:
x²-x-72
3x²-3x-168
Here is the way I have found to do these. First, make a couple of sets of parentheses.
( )( )
We put in the first letter. From X2 we can get ONLY X and X so put those in.
(X )(X ).
We next see that both of the signs are negative; therefore, the ONLY way we can get that is to have one of them + and one - so we put those in.
(X+ )(X- ).
The last number is done this way. Think of factors of 72 that multiply to give 72 but add (or subtract in this case) to give 1. Factors of 72 are 2*36; 3*24; 4*18; 6*12; 8*9. The ONLY one of those that has a chance of working is the last one BECAUSE, while all of them multiply to give 72, only the last set has a difference of 1 between the two. So we use 8 and 9 as the last numbers in the parentheses and place it so that the larger number gives a minus sign.
(X+8)(X-9) = X2-x-72. Now you try the last one and see if this doesn't work ok. Hint: I think 3 is a common factor so I would start with
3(X2-x-56) and factor the simpler set of numbers. Post your work if you get stuck and please tell us where you are having trouble. These can be daunting, at first, but practice, practice, and that makes things better.
1) x^2 -x-72 = (x-9)(x+8)
2) 3x^2 -3x-168 = 2(x^2 -x-56) --> (x-8)(x+7)
Thank you. I have the first figured out. But for the 2nd one, would it be (x-8)(x+7) or (3x-24)(3x+21)? Because I did x(squared)-x-56 to get (x-8)(x+7), but then don't you have to multiply it by the 3?
Nevermind, I understand it. It would be (x-8)(x+7) because you divided by the 3 to get 56. So, thanks!!!
I understand. Thank you!
You're welcome! I'm glad you were able to figure it out. Yes, in the second expression, you have correctly factored it as (x-8)(x+7). When you divided by 3 to simplify the expression, it affected the coefficient of the x term but not the factored form. So, the final answer is (x-8)(x+7), as you mentioned.
If you have any more questions or need further clarification, feel free to ask.