Dividing polynomials by synthetic division and rewriting using the division algorithm

The video tutorial explains how to divide polynomials using synthetic division. It begins with setting up the division by ensuring the divisor is in the form of X - K. The process involves taking the coefficients of the polynomial, performing synthetic division, and interpreting the results to find the quotient and remainder. The division algorithm is then used to express the polynomial division in a standard form.

What is the necessary form of the divisor for synthetic division?

• AX + K

• AX - K

• X - K

• X + K

In synthetic division, what should you do if a term is missing in the polynomial?

• Add a one for the missing term

• Add a zero for the missing term

• Repeat the previous term

• Ignore the missing term

What is the first step in the synthetic division algorithm?

• Multiply diagonally

• Add vertically

• Set the divisor to zero

• Drop down the first term

What does the remainder represent in the context of polynomial division?

• The divisor

• The quotient

• The original polynomial

• The leftover part after division

How can the original polynomial be expressed using the division algorithm?

• F(x) = D(x) * Q(x) + R(x)

• F(x) = D(x) / Q(x) + R(x)

• F(x) = D(x) + Q(x) + R(x)

• F(x) = D(x) * Q(x) - R(x)