PreCalculus Flashcard 2.2

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 do you determine the leading coefficient of a polynomial?

Back

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

Front

What does it mean if a polynomial has an even degree?

Back

If a polynomial has an even degree, its end behavior will be the same on both ends (either both go to positive infinity or both go to negative infinity).

Front

What does it mean if a polynomial has a positive leading coefficient?

Back

If a polynomial has a positive leading coefficient, the end behavior will rise to positive infinity as x approaches positive infinity.

Front

How do you find the zeros of a polynomial function?

Back

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

Front

What is the multiplicity of a zero?

Back

The multiplicity of a zero refers to the number of times a particular zero appears as a root of the polynomial.

Front

How do you write a polynomial given its zeros and degree?

Back

To write a polynomial given its zeros, use the factored form: for each zero, (x - zero) raised to the power of its multiplicity.

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity.

Front

What are the roots of the polynomial function y = (x + 2)(x - 7)³?

Back

The roots are -2 and 7, with 7 having a multiplicity of 3.

Front

What is the significance of the leading coefficient in determining the end behavior of a polynomial?

Back

The leading coefficient determines whether the ends of the polynomial will rise or fall as x approaches positive or negative infinity.