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

[Guest]

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.

[Guest]

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[Guest]

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 [tex]x^4+ px^3+ qx+ 5= (x+ 1)gx)+ 7[/tex] so, setting x= -1, [tex](-1)^4+ p(-1)^3+ q(-1)+ 5= 1- p- q+ 5= 1 or p+ q= 5.[/tex] 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 .

[GeradHum]

Use the Remainder Theorem:
f(−1) = 7 and f(2) = 1.
Set up equations:
(−1)^4 + p(−1)^3 + q(−1) + 5 = 7
2^4 + p(2)^3 + q(2) + 5 = 1
Solve the system for p and q.