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 a necessary condition for the division algorithm to apply to polynomials F(x) and D(x)?

• F(x) must be a linear polynomial.

• D(x) cannot be zero and its degree must be less than or equal to the degree of F(x).

• The degree of D(x) must be greater than the degree of F(x).

• D(x) must be a constant.

In the example where F(x) = 12 and D(x) = 4, what is the value of Q(x)?

• 5

• 2

• 3

• 4

If F(x) = 13 and D(x) = 4, what is the remainder R(x)?

• 0

• 3

• 2

• 1

What does Q(x) represent in the division algorithm?

• The remainder

• The dividend

• The quotient

• The divisor

How can all polynomials be expressed according to the division algorithm?

• As a product of the dividend and remainder

• As a difference between two polynomials

• As a product of the divisor and quotient plus the remainder

• As a sum of two polynomials