What is the division algorithm

The video tutorial explains the division algorithm for polynomials, stating that for polynomials F(X) and D(X), where D(X) is not zero and its degree is less than or equal to F(X), there exist unique polynomials Q(X) and R(X) such that F(X) = D(X) * Q(X) + R(X). If R(X) is zero, D(X) divides F(X) evenly. The tutorial provides examples with constant polynomials, demonstrating both cases where the remainder is zero and non-zero, and concludes by summarizing the division algorithm's format.

What is the division algorithm in the context of polynomials?

Explain the significance of the unique polynomials Q of X and R of X in the division algorithm.

If F of X = 12 and D of X = 4, what are the values of Q of X and R of X?

How does the remainder R of X relate to the divisibility of F of X by D of X?

Describe the general format of how polynomials can be expressed using the division algorithm.