Dividing two polynomials using synthetic division

The video tutorial explains synthetic division, a method used to divide polynomials. It begins by setting up the problem, ensuring the polynomial is in descending order and includes all necessary coefficients. The process involves using a binomial set to zero, extracting coefficients, and performing calculations by multiplying diagonally and adding vertically. The tutorial concludes by interpreting the results, highlighting that a zero remainder indicates the binomial divides evenly into the polynomial, and explaining how the coefficients form the quotient polynomial.

What is the first step in synthetic division when dealing with a binomial?

• Divide the polynomial by the binomial

• Add the binomial to the polynomial

• Set the binomial equal to zero

• Multiply the binomial by the polynomial

Why is it important to include coefficients for missing terms in a polynomial?

• To ensure the polynomial is in ascending order

• To maintain the correct degree of the polynomial

• To simplify the polynomial

• To ensure all terms are accounted for in calculations

What is the coefficient of the missing x cubed term in the example polynomial?

• -1

• 0

• 1

• 5

During synthetic division, what operation is performed after bringing down the first term?

• Subtract diagonally and divide vertically

• Add diagonally and multiply vertically

• Multiply diagonally and add vertically

• Divide diagonally and subtract vertically

What does a remainder of zero indicate in synthetic division?

• The division was performed incorrectly

• The polynomial has no real roots

• The binomial is a factor of the polynomial

• The polynomial is not divisible by the binomial