Final answer:
To divide the polynomials a(x) and b(x), we can use polynomial long division. The quotient polynomial q(x) is 5x^5 and the remainder polynomial r(x) is 0.
Step-by-step explanation:
To divide the polynomial a(x) by b(x), we can use polynomial long division. Divide the leading term of a(x) by the leading term of b(x) to get the first term of the quotient polynomial q(x). In this case, the leading term of a(x) is 5x^9 and the leading term of b(x) is x^4. Dividing these terms gives us q(x) = 5x^5.
Multiply b(x) by q(x) to get the product p(x). Subtract p(x) from a(x) to get the remainder polynomial r(x). In this case, p(x) = 5x^5 * x^4 = 5x^9 and r(x) = a(x) - p(x) = 5x^9 - 5x^9 = 0.
So, the quotient polynomial q(x) is 5x^5 and the remainder polynomial r(x) is 0.