SOLUTION: Hello Tutors, I am having trouble with the following problem. I have written some of my work and thoughts on this question out. Thank you very much for your attention and time i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello Tutors, I am having trouble with the following problem. I have written some of my work and thoughts on this question out. Thank you very much for your attention and time i      Log On


   

Question 101421: Hello Tutors,
I am having trouble with the following problem. I have written some of my work and thoughts on this question out. Thank you very much for your attention and time in helping me!
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1. A polynomial F, when divided by (x - 1), gives the remainder R1 = 2. The same polynomial F, when divided by (x + 1) gives the remainder R2 = 4. Find the remainder when F is divided by +%28x%5E2+-+1%29+. (Hint: Write the division statement when F is divided by +%28x%5E2+-+1%29+)
My work:
The division statement: +Q%28x%29+=+F%28x%5E2+-+1%29+
F%2F%28x+-+1%29+=+Q%28x%29+%2B+2
F%2F%28x+%2B+1%29+=+Q%28x%29+%2B+4

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.F%2F%28x+-+1%29+=+Q%28x%29+%2B+2
2.F%2F%28x+%2B+1%29+=+Q%28x%29+%2B+4
Use your own hint on the two equations.
x%5E2-1+=+%28x-1%29%28x%2B1%29
1. F%2F%28%28x-1%29%28x%2B1%29%29=Q%28x%29%2F%28x%2B1%29%2B2%2F%28x%2B1%29+
2. F%2F%28%28x-1%29%28x%2B1%29%29=Q%28x%29%2F%28x-1%29%2B4%2F%28x-1%29+
And then set both right hand sides equal to each other
Q%28x%29%2F%28x%2B1%29%2B2%2F%28x%2B1%29=Q%28x%29%2F%28x-1%29%2B4%2F%28x-1%29+
Then solve for Q(x). Then use it to solve for F(x).
I think that's enough to get you kick-started.
Submit another on if you get stuck again.