SOLUTION: I am helping a student study for a final in Intermediate Algebra. The problem is from a worksheet and only says "Simplify". I cannot figure out how to simplify the numerator. I tri

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am helping a student study for a final in Intermediate Algebra. The problem is from a worksheet and only says "Simplify". I cannot figure out how to simplify the numerator. I tri      Log On


   

Question 172562: I am helping a student study for a final in Intermediate Algebra. The problem is from a worksheet and only says "Simplify". I cannot figure out how to simplify the numerator. I tried factoring by grouping, but came up with nothing. Any help is greatly appreciated!!!
Here's the problem:
%28t%5E4-t%5E3-14t%5E2%2B7t-4%29%2F%28t-4%29

Found 2 solutions by Alan3354, Earlsdon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
%28t%5E4-t%5E3-14t%5E2%2B7t-4%29%2F%28t-4%29
---------------
No "simplification" is possible.
If you divide, you get t%5E3%2B3t%5E2-2t-1 with a remainder of -8.
However, if you change the last term to +4 instead of -4, it becomes
%28t-4%29%2A%28t%5E3+%2B+3t%5E2+-+2t+-+1%29
Maybe it's a typo.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:
%28t%5E4-t%5E3-14t%5E2%2B7t-4%29%2F%28t-4%29
Well, no wonder you're having trouble...the numerator is not factorable, and if you divide the numerator by the denominator, you get:
t%5E3%2B3t%5E2-2t-1 and a remainder of -8 so you can see that t-4 is not a factor of t%5E4-t%5E3-14%5E2t%2B7t-4 so I would have to conclude that the given fraction is already simplified.