Roots & Factors of Polynomials

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

How many roots can a polynomial of degree n have?

Back

A polynomial of degree n can have up to n roots, including real and complex roots.

Front

What is a real root?

Back

A real root is a solution to the polynomial equation that is a real number.

Front

What is an imaginary root?

Back

An imaginary root is a solution to the polynomial equation that is not a real number, often expressed in terms of the imaginary unit i.

Front

If a polynomial has a degree of 4, what can you say about its roots?

Back

A polynomial of degree 4 can have 4 real roots, or a combination of real and imaginary roots, such as 2 real and 2 imaginary.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial equation has at least one complex root.

Front

What is the difference between a polynomial and a monomial?

Back

A polynomial is a sum of one or more monomials, while a monomial is a single term with a non-negative integer exponent.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms.

Front

How do you determine the number of real roots of a polynomial?

Back

The number of real roots can be determined using the discriminant or by analyzing the graph of the polynomial.

Front

What is a factor of a polynomial?

Back

A factor of a polynomial is a polynomial that divides the original polynomial without leaving a remainder.