Polynomial Long Division Concepts

This video tutorial explains how to divide polynomials using long division. It covers the setup process, ensuring exponents are in descending order, and handling missing terms by inserting zeros. The tutorial walks through the steps of performing long division, focusing on multiplying and subtracting terms to find the quotient and remainder. It concludes with different ways to express the final answer, including writing the remainder as a rational expression.

When is it typically necessary to use long division for polynomials?

• When the polynomial is a monomial

• When the leading coefficient is 1

• When the leading coefficient is not 1 or dividing by a trinomial

• When dividing by a binomial

What should you ensure about the exponents when setting up a polynomial division?

• They are in descending order

• They are all even numbers

• They are in ascending order

• They are all odd numbers

What should you do if a polynomial term is missing when setting up the division?

• Ignore the missing term

• Add a zero for the missing degree

• Start the division without it

• Add a one for the missing degree

In the first step of long division, what do you focus on?

• The constant term

• The middle term

• The leading term of the divisor and dividend

• The entire polynomial

What operation follows multiplication in the long division process?

• Addition

• Subtraction

• Division

• Exponentiation

What is the next step after subtracting in polynomial long division?

• Multiply again

• Divide the terms

• Bring down the next term

• Add the terms

How do you determine what to multiply the divisor by in each step?

• By matching the middle terms

• By matching the leading terms

• By matching the constant terms

• By guessing

What is the remainder in polynomial division?

• The divisor

• The part of the dividend that is not divisible by the divisor

• The entire dividend

• The quotient

How can the remainder be expressed in the final answer?

• As a whole number

• As a decimal

• As a separate polynomial

• As a fraction over the divisor

What is the quotient in polynomial division?

• The dividend

• The result of the division

• The remainder

• The divisor