When the polynomial

Question

f(x)=(p-1)+x^3+px^2+qx+r, where p, q is divided by (x+2) and (x-1) the remainders are -5 and 4 respectively. If (x+1) is a factor of f(x), find the value of p, q and r, hence factorize f(x) completely.

Answer 1

from the given data:
f(x)=(p-1)+x^3+px^2+qx+r
f(1) = (p-1) + 1 + p + q + r = 4 ---> 2p + q + r = 4
f(-1) = (p-1) - 1 + p - q + r = 0 ----> 2p - q + r = 0
f(-2) = (p-1) - 8 + 4p - 2q + r = -5 --> 5p - 2q + r = -5

you now 3 equations in 3 unknowns, solve using your
favourite method, then factor the resulting f(x)

Answer 2

Not complete