Polynomials & End Behavior

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the degree of a polynomial?

Back

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

Front

What is the leading coefficient of a polynomial?

Back

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

Front

How does the degree of a polynomial affect its end behavior?

Back

The end behavior of a polynomial is determined by its degree and leading coefficient. Even degrees lead to the same end behavior on both sides, while odd degrees lead to opposite end behaviors.

Front

What is the end behavior of a polynomial with an even degree and a positive leading coefficient?

Back

As x → ∞, y → ∞ and as x → -∞, y → ∞.

Front

What is the end behavior of a polynomial with an odd degree and a positive leading coefficient?

Back

As x → ∞, y → ∞ and as x → -∞, y → -∞.

Front

What is the end behavior of a polynomial with an even degree and a negative leading coefficient?

Back

As x → ∞, y → -∞ and as x → -∞, y → -∞.

Front

What is the end behavior of a polynomial with an odd degree and a negative leading coefficient?

Back

As x → ∞, y → -∞ and as x → -∞, y → ∞.

Front

What does it mean for a polynomial to have a zero?

Back

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

Front

What is multiplicity in relation to polynomial zeros?

Back

Multiplicity refers to the number of times a particular zero appears as a root of the polynomial. A zero with an even multiplicity touches the x-axis, while a zero with an odd multiplicity crosses the x-axis.