Polynomial Long Division Concepts

The video tutorial explains how to divide polynomials using long division. It begins by setting up the division with zero terms for missing degrees, then proceeds through each step of the division process, focusing on calculating each term of the quotient. The tutorial concludes by demonstrating how to express the quotient with a remainder in different forms.

What is the purpose of including a zero term in the polynomial division setup?

• To increase the degree of the polynomial

• To simplify the polynomial

• To ensure like terms line up vertically

• To make the division process faster

How do you determine the first term of the quotient in polynomial long division?

• By adding the first terms of the dividend and divisor

• By subtracting the first term of the divisor from the first term of the dividend

• By multiplying the first terms of the dividend and divisor

• By dividing the first term of the dividend by the first term of the divisor

What operation is performed after multiplying the first term of the quotient with the divisor?

• Addition

• Subtraction

• Multiplication

• Division

In the second step of division, what is the next term in the quotient if the current term is negative two x squared?

• Two

• Negative two

• Negative two x

• Two x

What is the result of adding negative three x and positive four x?

• Zero

• Positive one x

• Negative seven x

• Positive seven x

What is the last term added to the quotient in the final step of division?

• One

• Three

• Zero

• Two

How is the remainder expressed in the quotient when using polynomial long division?

• As a separate term added to the quotient

• As a fraction over the divisor

• As a negative term in the quotient

• As a coefficient of the divisor

What is the remainder when dividing x cubed minus three x plus five by x plus two?

• One

• Two

• Three

• Four

Which of the following is a common way to express the quotient with a remainder?

• Quotient divided by remainder over divisor

• Quotient plus remainder over divisor

• Quotient minus remainder over divisor

• Quotient times remainder over divisor

What is the complete expression for the quotient of the given division problem?

• x squared plus two x plus one plus three over x plus two

• x squared plus two x minus one plus three over x plus two

• x squared minus two x plus one plus three over x plus two

• x squared minus two x minus one plus three over x plus two