Maths

When the polynomial
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.

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asked by Ande2
  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)

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