Understanding Synthetic Division

The video tutorial explains synthetic division, focusing on when to apply it, how to set it up, and the process of performing it. It emphasizes the importance of using placeholders for missing terms and demonstrates the calculation of the quotient and remainder. The tutorial concludes by verifying the results using the remainder theorem, ensuring the division was performed correctly.

What is the primary condition for using synthetic division?

• The divisor must be a quadratic polynomial.

• The divisor must be a linear polynomial.

• The dividend must be a quadratic polynomial.

• The dividend must be a constant.

What is the first step in setting up synthetic division?

• Finding the remainder

• Setting the divisor equal to zero

• Rewriting the polynomial

• Performing multiplication

Why is it necessary to rewrite the polynomial in descending order?

• To simplify the multiplication process.

• To ensure all terms are accounted for in synthetic division.

• To make the division process faster.

• To avoid using placeholders.

What is the role of placeholders in synthetic division?

• They are optional and can be ignored.

• They are used to simplify the divisor.

• They help in maintaining the correct order of terms.

• They are used to eliminate the remainder.

In synthetic division, what operation is performed on the diagonals?

• Multiplication

• Addition

• Division

• Subtraction

What is the result called when synthetic division is performed?

• Divisor

• Quotient

• Dividend

• Remainder

How is the remainder expressed in the final answer of synthetic division?

• As a coefficient of the highest degree term.

• As a fraction over the divisor.

• As a constant term in the quotient.

• As a separate term added to the quotient.

What theorem is used to verify the result of synthetic division?

• Division Theorem

• Remainder Theorem

• Factor Theorem

• Polynomial Theorem

What should be the result when the zero is plugged into the original function according to the remainder theorem?

• The quotient

• The divisor

• The remainder

• The dividend

What is the expected outcome if the divisor is a factor of the dividend?

• The remainder is zero.

• The quotient is zero.

• The dividend is zero.

• The divisor is zero.