The video tutorial explains how to use synthetic division to find function values and verify them using the remainder theorem. It demonstrates the process of synthetic division, emphasizing the importance of arranging terms in descending order and accounting for missing terms. The tutorial also highlights the verification of results by comparing the remainder from synthetic division with the value obtained by plugging the suspected zero into the function. The key takeaway is that both methods should yield the same remainder, ensuring the accuracy of the solution.

What is the purpose of using synthetic division in polynomial functions?

• To find the maximum value of the polynomial

• To calculate the integral of the polynomial

• To determine if a number is a zero of the polynomial

• To find the derivative of the polynomial

When applying synthetic division, what must you remember to include in the polynomial?

• The derivative of the polynomial

• All missing terms as zeros

• The highest degree term

• The constant term

What is the result of synthetic division if the number is a zero of the polynomial?

• The polynomial is undefined

• The remainder is equal to the polynomial's degree

• The quotient is zero

• The remainder is zero

How can you verify the result obtained from synthetic division?

• By checking if the quotient is a constant

• By using the remainder theorem to plug the number into the function

• By integrating the polynomial

• By calculating the derivative of the polynomial

What should you do if the remainder from synthetic division does not match the value obtained from the remainder theorem?

• Ignore the result and move on

• Change the suspected zero

• Recalculate using both methods to find the error

• Assume the polynomial is incorrect