Long Division of Polynomials: Challenging Examples

What is the divisor in the polynomial division example?

• X to the fourth minus X squared plus X minus four

• X squared minus 2X plus five

• Negative 13X plus 6

• X squared plus 2X minus 2

What role does the placeholder '0X cubed' play in polynomial long division?

• It ensures proper alignment of terms

• It simplifies the multiplication steps

• It increases the degree of the polynomial

• It represents an error in the polynomial

What should happen to the first term after subtracting in polynomial long division?

• It should become the remainder

• It should remain unchanged

• It should cancel out

• It should double in value

What is the result of subtracting '2X to the third' during the division process?

• 2X to the third

• Negative 4X squared

• Negative 2X squared

• 4X squared

How is the term '2X' used in the division process?

• To finalize the remainder

• To create a new polynomial

• As a divisor to reduce the highest term

• As a multiplier to balance the equation

What does a negative remainder indicate in polynomial long division?

• A need to reverse the division steps

• Incorrect calculations

• Subtraction was involved in the final steps

• The division was performed correctly

What is the degree of the remainder compared to the divisor when the division is complete?

• No remainder

• Lower degree

• Higher degree

• The same degree

What is the final remainder of the division?

• X squared minus 2X plus 5

• Negative 13X plus 6

• Zero

• X squared plus 2X minus 2

What should you ensure about the terms during polynomial long division?

• They are in descending order

• They are all positive

• They are in ascending order

• They are multiplied by zero

What is the importance of placeholders like '0X cubed' in polynomial long division?

• To increase the complexity

• To act as divisors

• To fill missing degrees for alignment

• To reduce the number of terms