Understanding the Remainder Theorem

The video tutorial explains the remainder theorem, which helps determine if a binomial is a factor of a polynomial. It provides four examples: checking if x + 2, x - 1, x, and 2x - 3 are factors of given polynomials. The process involves evaluating the polynomial function at specific values derived from the binomial and checking if the result is zero, indicating the binomial is a factor.

What does the Remainder Theorem state about the remainder when a polynomial f(x) is divided by x - c?

• The remainder is x - c.

• The remainder is f(x).

• The remainder is f(c).

• The remainder is always zero.

In Example 1, what is the value of c when determining if x + 2 is a factor?

• -2

• 1

• 2

• 0

What is the function value f(-2) in Example 1, and what does it indicate?

• f(-2) = 1, indicating x + 2 is not a factor.

• f(-2) = 2, indicating x + 2 is not a factor.

• f(-2) = 0, indicating x + 2 is a factor.

• f(-2) = -1, indicating x + 2 is a factor.

In Example 2, what is the function value f(1) and what does it imply about x - 1?

• f(1) = 0, x - 1 is a factor.

• f(1) = 20, x - 1 is not a factor.

• f(1) = -20, x - 1 is a factor.

• f(1) = 1, x - 1 is not a factor.

In Example 3, what is the function value f(0) and what does it indicate about x?

• f(0) = 0, x is a factor.

• f(0) = -1, x is not a factor.

• f(0) = 1, x is a factor.

• f(0) = 2, x is not a factor.

In Example 4, what is the adjusted form of the binomial 2x - 3 to apply the Remainder Theorem?

• x - 1

• x - 2

• x - 3

• x - 3/2

What is the function value f(3/2) in Example 4, and what does it indicate about 2x - 3?

• f(3/2) = 0, 2x - 3 is a factor.

• f(3/2) = 1, 2x - 3 is not a factor.

• f(3/2) = -1, 2x - 3 is a factor.

• f(3/2) = 2, 2x - 3 is not a factor.

What is the significance of the function value being zero when using the Remainder Theorem?

• It means the binomial is a factor.

• It means the binomial is not a factor.

• It means the polynomial is zero.

• It means the polynomial is undefined.

How can you determine the value of c when the binomial is in the form x + a?

• Set x + a equal to zero and solve for x.

• Set x - a equal to zero and solve for x.

• Set x + a equal to one and solve for x.

• Set x - a equal to one and solve for x.

What happens if the function value is not zero when applying the Remainder Theorem?

• The polynomial is zero.

• The polynomial is undefined.

• The binomial is not a factor.

• The binomial is a factor.