by Guest » Sat Sep 21, 2019 1:33 pm
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. 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 .