Question

Dividing x3 + 3x2 + 3x +1 by 5 + 2x and verify the division algorithm.

Answer 1

Let f(x) = -x3 + 3x2 - 3x + 5 and g(x) = -x2 + x - 1.

We have:

Quotient, q(x) = x - 2 and remainder, r(x) = 3.

Now,

Quotient Divisor + Remainder.

= (x - 2)(-x2 + x - 1) + 3.

= -x3 + x2 - x + 2x2 - 2x + 2 + 3.

= -x3 + 3x2 - 3x + 5 = Dividend.