Rational Roots - practice

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 p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient.

Front

List the possible rational roots for the polynomial f(x) = 3x^5 - 5x^2 + x + 6.

Back

±1, ±2, ±3, ±6, ±1/3, ±2/3.

Front

How do you determine if (x - c) is a factor of a polynomial f(x)?

Back

Use synthetic division or polynomial long division. If the remainder is zero, then (x - c) is a factor.

Front

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

Back

±1, ±3, ±9, ±1/2, ±3/2, ±9/2.

Front

What is a rational zero?

Back

A rational zero is a solution to a polynomial equation that can be expressed as a fraction p/q, where p and q are integers.

Front

What is the significance of the constant term in finding rational roots?

Back

The constant term provides the possible values for p in the Rational Root Theorem, as p must be a factor of this term.

Front

What is the leading coefficient in a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in the polynomial.

Front

If f(x) = x^3 + 2x^2 - 6x + 8, what are the possible rational roots?

Back

±1, ±2, ±4, ±8.

Front

What does it mean if a polynomial has a remainder of zero when divided by (x - c)?

Back

It means that c is a root of the polynomial, and (x - c) is a factor of the polynomial.

Front

How can you verify if a number is a rational root of a polynomial?

Back

Substitute the number into the polynomial. If the result is zero, then it is a rational root.