Dividing Polynomials with Synthetic Division

The video tutorial introduces synthetic division, highlighting its efficiency compared to long division. It explains the conditions necessary for using synthetic division, such as having a linear binomial divisor. The tutorial guides viewers through setting up the division by arranging the dividend in standard form and using coefficients. It then demonstrates the step-by-step process of performing synthetic division and interpreting the results, including handling remainders.

What is one major advantage of synthetic division over long division?

• It simplifies the process by reducing the amount of work.

• It can be used for any type of divisor.

• It always gives an exact answer.

• It can be used for both polynomials and rational functions.

Which type of divisor is required for synthetic division?

• Any polynomial

• Cubic polynomial

• Linear binomial

• Quadratic binomial

Why can't synthetic division be used with a divisor like x^2 + 4?

• Because it has more than two terms.

• Because it has a constant term.

• Because it is not linear.

• Because it is not a binomial.

What must be done to the dividend before using synthetic division?

• It must be divided by the leading coefficient.

• It must be factored completely.

• It must be converted to a quadratic form.

• It must be written in standard form with descending order of degrees.

What should you do if a term is missing in the dividend when setting up the synthetic division box?

• Repeat the previous term.

• Add a one in place of the missing term.

• Add a zero in place of the missing term.

• Ignore the missing term.

What is the first step in the synthetic division process?

• Multiply the divisor by the first coefficient.

• Bring down the first coefficient as a freebie.

• Set the divisor equal to zero.

• Add the first two coefficients.

In synthetic division, what operation is performed when moving diagonally?

• Division

• Subtraction

• Addition

• Multiplication

What is the result of adding 26 and -20 in the synthetic division example?

• 6

• 46

• 4

• 0

How is the final answer structured in synthetic division?

• Quadratic, linear, constant, remainder

• Constant, linear, quadratic, remainder

• Linear, quadratic, constant, remainder

• Remainder, constant, linear, quadratic

What should you do with the remainder in the final answer?

• Ignore it.

• Add it to the constant term.

• Write it as a fraction over the divisor.

• Multiply it by the divisor.