Dividing Polynomials with Synthetic Division: Handling Missing Terms

The video tutorial introduces synthetic division, explaining its prerequisites and setup. It covers the importance of having the divisor in the form of x - K and setting up the polynomial in descending order with all coefficients. The tutorial provides a step-by-step guide on performing synthetic division, including interpreting the results and understanding the remainder. It concludes with a discussion on the limitations of synthetic division and hints at further learning opportunities.

What is the first requirement for using synthetic division?

• The divisor must be in the form of x + k.

• The divisor must be in the form of x - k.

• The polynomial must be linear.

• The polynomial must be quadratic.

How should the polynomial be arranged before performing synthetic division?

• In descending order of degrees.

• In random order.

• In ascending order of degrees.

• In alphabetical order.

What should you do if a term is missing in the polynomial?

• Add a placeholder with a coefficient of zero.

• Ignore the missing term.

• Add a placeholder with a coefficient of one.

• Repeat the previous term.

What is the first step in the synthetic division process?

• Subtract the first coefficient from the divisor.

• Bring down the first coefficient.

• Add the first coefficient to the divisor.

• Multiply the divisor by the first coefficient.

What operation is performed when moving diagonally in synthetic division?

• Multiplication

• Subtraction

• Division

• Addition

What is the result of adding -16 and 18 in the synthetic division process?

• -34

• 34

• -2

• 2

What does the last term in the synthetic division result represent?

• The remainder

• The constant term

• The linear term

• The quadratic term

How should you interpret the terms in the synthetic division result?

• From the highest degree to the lowest degree

• From the lowest degree to the highest degree

• In random order

• In alphabetical order

What is a necessary condition for using synthetic division?

• The divisor must be a binomial.

• The polynomial must be linear.

• The polynomial must be quadratic.

• The divisor must be a trinomial.

Can synthetic division be used if the divisor is not in the form of x - k?

• Yes, always.

• No, never.

• Yes, but only if the polynomial is quadratic.

• Yes, but only if the polynomial is cubic.