Use the division algorithm to find qx and rx such that ax q

Use the division algorithm to find q(x) and r(x) such that a(x) = q(x)b(x) + r(x) with deg r(x)

Solution

To satisfy the equation a(x) = q(x)*b(x) + r(x), we just need to find the quotient and remainder when a(x) is divided by b(x)
Quotient will be q(x) and remainder will be r(x)

  (x⁵ + x³ - x² - x ) / x³ + x

x⁵ + x³ - x² - x can be written as (x³ + x)(x²) - x² - x
So q(x) = x² and r(x) = -x² - x