Factoring and Zeros Flashcard

Front

What is the result of dividing a polynomial by a monomial?

Back

The result is a polynomial where each term of the original polynomial is divided by the monomial.

Front

What does it mean for a set to be closed under an operation?

Back

A set is closed under an operation if performing that operation on members of the set always produces a member of the same set.

Front

What is a quadratic inequality?

Back

A quadratic inequality is an inequality that involves a quadratic expression, typically in the form ax² + bx + c < 0 or ax² + bx + c > 0.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for the variable.

Front

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

Back

The leading coefficient determines the end behavior of the polynomial function.

Front

What is the difference between a polynomial and a monomial?

Back

A polynomial is a sum of multiple terms, while a monomial consists of only one term.

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

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the relationship between the roots and the factors of a polynomial?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero, and each root corresponds to a factor of the polynomial.