Polynomial Remainder and Factor Theorems

This video tutorial covers the remainder and factor theorems for polynomials. It begins with an introduction to these theorems, explaining how the remainder theorem allows for quick calculation of remainders by substituting values into polynomials. The video then demonstrates using the remainder theorem to evaluate functions at specific values and introduces the factor theorem, which builds on the remainder theorem by identifying factors when the remainder is zero. The tutorial concludes with examples of determining zeros of polynomials using these theorems.

What is the main purpose of the Remainder Theorem?

• To find the roots of a polynomial

• To determine if a polynomial is divisible by another

• To quickly find the remainder of a polynomial division

• To factorize a polynomial completely

How can you find the remainder when dividing a polynomial by x - a?

• By factoring the polynomial

• By using the quadratic formula

• By substituting a into the polynomial

• By performing long division

What is the remainder when the polynomial is evaluated at x = 3?

• 3

• 107

• 0

• Cannot be determined

What is the alternative method to evaluate a polynomial at a specific value using the Remainder Theorem?

• Using integration

• Using the binomial theorem

• Using the quadratic formula

• Using synthetic division

What is the remainder when the polynomial is evaluated at x = -2 using synthetic division?

• 2

• -10

• 10

• 0

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

• The polynomial has no real roots

• The polynomial is a constant

• The divisor is a factor of the polynomial

• The polynomial is prime

How can you determine if x + 4 is a factor of a polynomial?

• By using the quadratic formula

• By graphing the polynomial

• By finding the derivative of the polynomial

• By checking if the remainder is zero when divided by x + 4

What is the remainder when the polynomial is divided by x + 4?

• -4

• 0

• Cannot be determined

• 4

If x - 2 is a factor of a polynomial, what should the remainder be when divided by x - 2?

• 2

• Cannot be determined

• 0

• -2

What conclusion can be drawn if the remainder is not zero when dividing by x - 2?

• The polynomial is quadratic

• x - 2 is a factor

• x - 2 is not a factor

• The polynomial is constant