Test 3 - Rational Root Theorem

Front

What does the degree of a polynomial indicate?

Back

The degree of a polynomial indicates the maximum number of roots (solutions) it can have.

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution (root) of a polynomial equation is of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Front

How do you determine if a number is a root of a polynomial?

Back

To determine if a number is a root of a polynomial, substitute the number into the polynomial. If the result is zero, then it is a root.

Front

What are the possible rational roots of the polynomial f(x) = 2x^3 - 3x^2 + 4?

Back

The possible rational roots can be found by taking the factors of the constant term (4) and the leading coefficient (2). Possible roots: ±1, ±2, ±4, ±1/2.

Front

If f(x) = x^3 - 6x^2 + 11x - 6, what are the roots?

Back

The roots are 1, 2, and 3.

Front

What is a zero of a polynomial function?

Back

A zero of a polynomial function is a value of x for which the polynomial evaluates to zero.

Front

How can you find the zeros of a polynomial?

Back

You can find the zeros of a polynomial by factoring the polynomial, using synthetic division, or applying the Rational Root Theorem.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor.

Front

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

Back

The leading coefficient determines the end behavior of the polynomial function and influences the shape of its graph.

Front

What is the relationship between the number of roots and the degree of a polynomial?

Back

A polynomial of degree n can have up to n roots, counting multiplicities.