Exploring Synthetic Division and the Remainder Theorem

The video tutorial explains how to use the remainder theorem to find the value of a function at a specific point, f(3), by performing synthetic division. It begins with an introduction to the problem, followed by a detailed explanation of the remainder theorem. The tutorial then walks through the steps of synthetic division, including switching signs and writing down coefficients. It provides a detailed calculation process, ensuring accuracy through verification. The video concludes by confirming the result using the remainder theorem, demonstrating that f(3) equals 240.

What is the main goal of the problem presented in the video?

• To find the roots of the polynomial.

• To solve a quadratic equation.

• To find the value of f(3) using the remainder theorem.

• To factorize the polynomial.

According to the remainder theorem, what is f(3) equal to?

• The quotient when the polynomial is divided by x-3.

• The remainder when the polynomial is divided by x-3.

• The product of the polynomial and x-3.

• The sum of the polynomial and x-3.

What is the first step in synthetic division?

• Add the coefficients together.

• Switch the sign of the divisor.

• Multiply the coefficients by 3.

• Divide the coefficients by 3.

What are the coefficients of the polynomial used in the synthetic division?

• 1, -5, 5, -6

• 1, 5, 5, -6

• 1, 5, 5, 6

• 1, 5, -5, -6

What is the result of multiplying 1 by 3 in the synthetic division process?

• 1

• 3

• 5

• 8

What is the sum of 8 and 24 in the synthetic division process?

• 31

• 32

• 29

• 30

What is the product of 29 and 3 in the synthetic division process?

• 87

• 90

• 84

• 81

What is the final remainder when the polynomial is divided by x-3?

• 82

• 240

• 246

• 87

What does the remainder theorem state about the remainder when dividing by x-3?

• It is equal to the product.

• It is equal to the divisor.

• It is equal to the quotient.

• It is equal to f(3).

What is the value of f(3) as found in the video?

• 246

• 82

• 240

• 87