How to use the remainder and factor theorem for polynomials

The video tutorial explains the remainder and factor theorems, focusing on how to determine if a number is a zero of a polynomial. It demonstrates the process using an example calculation with F(3) and discusses the implications of the remainder theorem. The tutorial emphasizes the relationship between factors and zeros, providing a clear understanding of these mathematical concepts.

What does the factor theorem state about a polynomial and its zeros?

• If (x + k) is a factor, then k is a zero.

• If (x + k) is a factor, then k is not a zero.

• If (x - k) is a factor, then k is a zero.

• If (x - k) is a factor, then k is not a zero.

In the example provided, what is the result of F(3) for the polynomial?

• F(3) = 7

• F(3) = 0

• F(3) = 3

• F(3) = 5

What conclusion can be drawn if F(3) equals zero for a polynomial?

• 3 is not a zero of the polynomial.

• 3 is a zero, and (x - 3) is a factor.

• 3 is a zero, but (x - 3) is not a factor.

• 3 is not a zero, but (x - 3) is a factor.

According to the remainder theorem, what does a non-zero result indicate when a number is plugged into a polynomial?

• The number is a zero of the polynomial.

• The number is not a factor, and the result is zero.

• The number is not a zero, and the result is the remainder.

• The number is a factor of the polynomial.

If F(4) equals 7, what does the remainder theorem suggest about the division of the polynomial by (x - 4)?

• The remainder is 1.

• The remainder is 7.

• The remainder is 4.

• The remainder is 0.