The polynomial p(x) = 4x^3 + bx^2 + cx + 11 has a remainder of -7 when divided by (x + 2) and a remainder of 14 when divided by (x - 1).

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Remainder theorem states that if f(x) is divided by x-k , then the remainder is f(k) Use that , for the first one you get ,plugging x=-2 -32+4b-2c+11=-7 4b-2c=14 For the second one , plug in x=1 4+b+c+11=14 b+c=-1 solving them you get b=2 and c=-3