Applying synthetic division to a polynomial with missing terms

The video tutorial explains how to determine if X - 1 divides evenly into the polynomial X to the fifth plus seven using synthetic division. It begins by setting up the polynomial and identifying missing terms, then proceeds with the synthetic division process, detailing each step and calculation. The tutorial concludes by interpreting the results, including the remainder and quotient, and summarizing the division process.

What is the main goal when analyzing the polynomial X to the fifth plus seven in the context of this lesson?

• To graph the polynomial

• To determine if X - 1 divides evenly into it

• To find the roots of the polynomial

• To calculate the derivative of the polynomial

Which term is missing in the polynomial X to the fifth plus seven when preparing it for synthetic division?

• All of the above

• X to the fourth

• X squared

• X cubed

What is the first step in applying synthetic division to the polynomial?

• Divide the constant term

• Drop down the first term

• Multiply the coefficients

• Add the remainder

What is the remainder when X - 1 is divided into X to the fifth plus seven using synthetic division?

• 1

• 0

• 8

• 7

What is the quotient polynomial obtained after dividing X to the fifth plus seven by X - 1?

• X to the fourth plus X cubed minus X squared plus X minus 1

• X to the fourth plus X cubed plus X squared plus X plus 1

• X to the fourth minus X cubed plus X squared minus X plus 1

• X to the fourth minus X cubed minus X squared minus X minus 1