Question

What must be added to p(x) = 4x^4-5x^3-39x^2-46x-2 so that the resulting polynomial is divisible by g(x) = 4x^2 7 x 2 ?

Answer 1

The remainder is (3x + 1)
Hence [ – (3x + 1)] should be added to 3x4+ 5x3 – 7x2 + 5x + 3 so that the resulting polynomial is exactly divisible by (x2+3x+1).