How to use the Remainder Theorem with Polynomials

What is a common issue when using synthetic division on polynomials with missing terms?

• It always results in fractions.

• It can be time-consuming.

• It simplifies the process.

• It requires additional steps.

According to the Remainder Theorem, what is the remainder when a polynomial f(x) is divided by x-k?

• x

• f(x)

• f(k)

• k

What does the Factor Theorem state about a polynomial if the remainder is zero?

• The polynomial is undefined.

• The polynomial has no real roots.

• x-k is a factor of the polynomial.

• The polynomial is prime.

How can you determine if x-k is a factor of a polynomial using the Factor Theorem?

• By finding the derivative of the polynomial.

• By checking if the remainder is zero.

• By using long division.

• By graphing the polynomial.

What is a key step when dealing with fractions in the Remainder Theorem?

• Multiplying by zero.

• Ignoring the fractions.

• Using synthetic division.

• Finding a common denominator.

Why might students prefer using the Remainder Theorem over synthetic division with fractions?

• It is faster.

• It is more accurate.

• It is less prone to errors.

• It avoids complex calculations.

What is the remainder when evaluating f(1/2) for a polynomial using the Remainder Theorem?

• 1

• 11/8

• 1/2

• 0