Dividing two polynomials using synthetic division

The video tutorial explains how to apply synthetic division to determine if a binomial divides a polynomial evenly. It covers setting up the division, performing the calculations, and interpreting the results, including identifying the quotient and remainder.

What is the necessary condition for a divisor in synthetic division?

• It must be a constant.

• It must be a trinomial.

• It must have a variable to the second power.

• It must be a binomial with the variable to the first power.

Why is it important to arrange the polynomial in descending order before starting synthetic division?

• To avoid errors in calculations.

• To ensure the coefficients are correct.

• To ensure all terms are accounted for, including missing ones.

• To make the division process faster.

What is the first step in the synthetic division algorithm?

• Add vertically.

• Multiply diagonally.

• Set the divisor equal to zero.

• Bring down the first coefficient.

What does a remainder of zero indicate in synthetic division?

• The divisor is not a factor of the polynomial.

• The divisor is a factor of the polynomial.

• The polynomial is incomplete.

• The division process was incorrect.

How is the resulting polynomial written after completing synthetic division?

• As a difference between the original polynomial and the divisor.

• As a quotient divided by the divisor.

• As a sum of the original polynomial and the divisor.

• As a product of the divisor and the quotient.