Polynomial Functions and Their Properties

The video tutorial explains the rational roots test, a method to find possible rational roots of a polynomial by examining the factors of the constant term and the leading coefficient. It demonstrates the process with an example polynomial, showing how to list possible rational roots and verify them through substitution. The tutorial also identifies actual roots and discusses how to factor the polynomial using these roots.

What is the purpose of the Rational Roots Test?

• To solve a polynomial equation.

• To factor a polynomial completely.

• To determine if a polynomial has any rational roots.

• To find all roots of a polynomial.

Which of the following is NOT a requirement for using the Rational Roots Test?

• The polynomial must have a leading coefficient.

• The polynomial must have a constant term.

• The polynomial must be quadratic.

• The polynomial must have integer coefficients.

How do you determine the possible rational roots of a polynomial?

• By solving the polynomial equation directly.

• By finding the factors of the constant term and the leading coefficient.

• By using the quadratic formula.

• By graphing the polynomial.

What are the factors of the constant term in the polynomial 2x^3 - 3x^2 - 11x + 6?

• 1, 2, 3, 6

• 1, 2

• 1, 3, 6

• 1, 2, 3

What are the factors of the leading coefficient in the polynomial 2x^3 - 3x^2 - 11x + 6?

• 1, 2, 3

• 1, 2

• 1, 3

• 1, 6

What is the first step in using the Rational Roots Test?

• Use the quadratic formula.

• Graph the polynomial.

• Solve the polynomial equation.

• Identify the factors of the constant term.

What is the second step in using the Rational Roots Test?

• Identify the factors of the leading coefficient.

• Solve the polynomial equation.

• Graph the polynomial.

• Use the quadratic formula.

What is the final step in using the Rational Roots Test?

• List all possible combinations of factors.

• Solve the polynomial equation.

• Graph the polynomial.

• Use the quadratic formula.

What is the definition of a rational number?

• A number that is always negative.

• A number that is always positive.

• A number that cannot be expressed as a fraction.

• A number that can be expressed as a fraction.

Which of the following is a possible rational root of the polynomial 2x^3 - 3x^2 - 11x + 6?

• 1/2

• 7

• 5

• 4