Why and how to we apply synthetic division with a missing term

The video tutorial explains the process of determining if a divisor is a factor of a polynomial. It covers setting up the polynomial division with placeholders for missing terms, performing the division step-by-step, and understanding the role of remainders. The tutorial emphasizes the importance of maintaining place value and descending order in polynomial terms to ensure accurate results. The final section discusses how to write the solution and verify the correctness of the division.

What is the first step in determining if a divisor is a factor of a polynomial?

• Set the divisor equal to zero and solve for x.

• Multiply the divisor by the polynomial.

• Add the divisor to the polynomial.

• Subtract the divisor from the polynomial.

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

• To ensure the polynomial is in ascending order.

• To make the polynomial easier to read.

• To maintain the correct place value and order.

• To increase the degree of the polynomial.

What happens if you do not include zero coefficients in a polynomial during division?

• The polynomial becomes longer.

• The final answer remains unchanged.

• The polynomial becomes a constant.

• The final answer may be incorrect.

In polynomial division, what is the significance of the remainder?

• It determines the degree of the polynomial.

• It indicates whether the divisor is a factor.

• It changes the leading coefficient.

• It simplifies the polynomial.

How is the final expression of a polynomial division result written?

• By ignoring all zero coefficients.

• By multiplying the divisor by the quotient.

• By including all terms with their coefficients.

• By only writing the remainder.