What is the Remainder Theorem

The video tutorial explains the remainder theorem, which states that if a polynomial f(x) is divided by a factor (x - k), the remainder is f(k). The instructor demonstrates this using synthetic division and evaluates the polynomial to show that the remainder is zero when the factor is a true divisor. The video highlights the importance of the theorem in determining factors without full division and provides multiple examples to illustrate the concept.

What does the Remainder Theorem state about the remainder when a polynomial F(x) is divided by a factor (x - K)?

• The remainder is always zero.

• The remainder is equal to F(K).

• The remainder is equal to K.

• The remainder is equal to the degree of the polynomial.

In the example provided, what is the remainder when the polynomial is divided by the factor (x + 3)?

• 0

• 5

• 7

• 3

How can you verify if a factor divides a polynomial evenly without performing division?

• By evaluating the polynomial at the zero of the factor.

• By finding the derivative of the polynomial.

• By checking if the polynomial is prime.

• By multiplying the polynomial by the factor.

What is the result of evaluating F(2) in the final example?

• 34

• 0

• 10

• 20

Why is the Remainder Theorem considered useful?

• It helps in graphing polynomials.

• It allows for quick verification of factors without division.

• It simplifies the process of finding polynomial roots.

• It provides a method to calculate derivatives.