Rational Zeros and Polynomial Functions

The video tutorial explains the rational zero theorem, which helps list possible rational zeros of a polynomial function. It provides three examples demonstrating how to find these zeros using synthetic division and the quadratic formula. The tutorial emphasizes the importance of identifying possible zeros and verifying them to solve polynomial equations effectively.

What is the main purpose of the Rational Zero Theorem?

• To determine the degree of a polynomial

• To find the derivative of a polynomial

• To factor a polynomial completely

• To list all possible rational zeros of a polynomial

In the polynomial f(x) = x^3 + 2x^2 - 5x - 6, what are the possible rational zeros?

• 0, 1, 2, 3

• 1, -1, 2, -2

• 2, 4, 6, 8

• 1, 2, 3, 6

Which method is used after finding the first zero in a polynomial to find the remaining zeros?

• Synthetic division

• Integration

• Long division

• Differentiation

What is the constant term in the polynomial f(x) = x^3 + 2x^2 - 5x - 6?

• -6

• 2

• -5

• 1

What is the first zero found for the polynomial f(x) = x^3 + 8x^2 + 11x - 20?

• x = 2

• x = -1

• x = 1

• x = 0

After using synthetic division on f(x) = x^3 + 8x^2 + 11x - 20, what is the resulting quadratic expression?

• x^2 + 9x + 20

• x^2 + 6x + 9

• x^2 + 8x + 11

• x^2 + 7x + 10

What is the leading coefficient in the polynomial f(x) = x^3 + 8x^2 + 11x - 20?

• 8

• 11

• -20

• 1

For the polynomial f(x) = x^3 - 11x + 6, what is the first zero found?

• x = 4

• x = 2

• x = 3

• x = 1

Which formula is used to find the remaining zeros of f(x) = x^3 - 11x + 6 when it cannot be factored?

• Quadratic formula

• Cubic formula

• Factorization method

• Synthetic division

What are the two other zeros found using the quadratic formula for f(x) = x^3 - 11x + 6?

• x = -2 ± √15/2

• x = -4 ± √19/2

• x = -3 ± √17/2

• x = -1 ± √13/2