# Polynomials- can someone help me with this problem, please?

### Polynomials- can someone help me with this problem, please?

Let f(x) = x^4+px^3+qx+5, where p, q are constants. The remainder when f(x) is divided by (x+1) is 7, and the remainder when f(x) is divided by (x-2) is 1. Find the value of p and the value of q.
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### Re: Polynomials- can someone help me with this problem, plea

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### Re: Polynomials- can someone help me with this problem, plea

In response to the first post (the second seems to be spam), if "f(x) divided by p(x) has quotient g(x) and remainder r" then f(x)= p(x)g(x)+ r. In particular, if p(x)= x- a then f(x)= (x- a)g(x)+ r so, setting x= a, f(a)= r. Here, we have $$x^4+ px^3+ qx+ 5= (x+ 1)gx)+ 7$$ so, setting x= -1, [tex](-1)^4+ p(-1)^3+ q(-1)+ 5= 1- p- q+ 5= 1 or p+ q= 5. Do the same with [tex]x^4+ px^3+ qx+ 5= (x-2)g(x)+ 1[tex]. setting x= 2 to get another equation in p and .
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### Re: Polynomials- can someone help me with this problem, plea

[quote]I really don't want people to just post their math problems here and just wait for an answer.[quote]
Yes, because you would much rather people payed you money to do what people here do for free!
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