Question

find the remainder when 4 x 4 - 3 x cube minus 2 X square + X - 7 is divided by 2 X + 1​

Answer 1

As a concrete example of p, a, q, and r, let's look at the polynomial p(x) = x3 – 7x – 6, and let's divide by the linear factor x – 4 (so a = 4):

completed division: quotient x^2 + 4x + 9, remainder 30

So we get a quotient of q(x) = x2 + 4x + 9 on top, with a remainder of r(x) = 30.