Polynomial Long Division Concepts

The video tutorial explains how to perform polynomial long division. It begins by setting up the division problem, ensuring all terms are aligned, including zero terms for missing degrees. The process involves dividing the leading terms, multiplying, and subtracting, similar to long division with numbers. Each step is repeated until all terms are used, resulting in a quotient and a remainder. The final answer is expressed as a polynomial plus the remainder over the divisor. The tutorial emphasizes the importance of aligning terms and provides tips for expressing the final answer in different forms.

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

• To avoid using subtraction

• To simplify the divisor

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

• By subtracting the divisor from the dividend

• By adding the terms of the dividend

• By multiplying the divisor by the dividend

Why is it important to change subtraction to addition of the opposite in polynomial long division?

• It simplifies the multiplication process

• It helps in aligning the terms correctly

• It makes the subtraction process easier

• It reduces the number of steps required

What is the result of adding 11x^3 and -6x^3 during the division process?

• 5x^3

• 17x^3

• 0

• -5x^3

What is the next step after obtaining a negative 30x^2 in the division process?

• Multiply by the divisor

• Bring down the next term

• Add the opposite

• Divide by the next term

How do you handle a negative term in the quotient during polynomial long division?

• Ignore it

• Multiply it by the divisor

• Add it to the dividend

• Subtract it from the dividend

What is the remainder when the division process is complete?

• 6

• 0

• 12

• 3

How is the remainder expressed in the final answer of polynomial long division?

• As a part of the quotient

• As a negative number

• As a fraction over the divisor

• As a separate term

What is the final quotient obtained from the division process?

• x^3 - 5x^2 + 30x - 2

• x^3 + 5x^2 + 30x + 2

• x^3 + 5x^2 - 30x + 2

• x^3 - 5x^2 - 30x - 2

If the remainder was negative, how would it be expressed in the final answer?

• As a separate term

• As a positive fraction

• As a subtraction from the quotient

• As an addition to the quotient