Question

Divide the polynomial p(x) by the polynomial g(x) and find the quotient q(x) and remainder r(x) in p(x) = x⁶ + x⁴ + x³ + x² + 2x + 2, g(x) = x³ + 1

Answer 1

p(x) = x⁶ + x⁴ + x³ + x² + 2x + 2, g(x) = x³ + 1

Dividend = x⁶ + x⁴ + x³ + x² + 2x + 2

Divisor = x³ + 1

Here, dividend and divisor both are in the standard form.

Now, on dividing p(x) by g(x) we get the following division process we get,

q(x) = x³ + x

r(x) = x² + x + 2