BAIT #77 A2H

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution (or root) of a polynomial equation, in the form of \( \frac{p}{q} \), has \( p \) as a factor of the constant term and \( q \) as a factor of the leading coefficient.

Front

What are the possible rational roots of the polynomial \( x^3 - 6x^2 - x + 30 \)?

Back

The possible rational roots can be found using the Rational Root Theorem. In this case, one possible rational root is \( -15 \).

Front

How do you determine possible positive roots of a polynomial?

Back

To find possible positive roots, evaluate the polynomial function \( f(x) \).

Front

How do you determine possible negative roots of a polynomial?

Back

To find possible negative roots, evaluate the polynomial function \( f(-x) \).

Front

What are the possible rational roots of the polynomial \( 2x^3 - 11x^2 + 12x + 9 = 0 \)?

Back

The possible rational roots are: \( \pm 1, \pm 3, \pm 9, \pm \frac{1}{2}, \pm \frac{3}{2}, \pm \frac{9}{2} \).

Front

Solve the polynomial equation using the Rational Root Theorem: \( 2x^3 - 11x^2 + 12x + 9 = 0 \).

Back

The solutions are: \( -\frac{1}{2}, 3, 3 \).

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What is a rational root?

Back

A rational root is a solution to a polynomial equation that can be expressed as a fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It affects the end behavior of the polynomial function.

Front

What does it mean for a polynomial to have a degree of 3?

Back

A polynomial of degree 3 is a cubic polynomial, which means its highest exponent is 3. It can have up to 3 real roots.