2.8 Graphing Polynomials

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its factors, which can include linear factors and irreducible polynomials.

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

What does the multiplicity of a zero refer to?

Back

Multiplicity of a zero refers to how many times a particular zero (or root) appears in the factored form of a polynomial.

Front

How do you determine the degree of a polynomial?

Back

The degree of a polynomial is determined by the highest exponent of the variable in the polynomial.

Front

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

Back

The leading term determines the end behavior of the polynomial function as x approaches positive or negative infinity.

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero.

Front

How can you find the zeros of a polynomial?

Back

You can find the zeros of a polynomial by factoring it and setting each factor equal to zero.

Front

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

Back

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

Front

What does it mean for a polynomial to have a double root?

Back

A double root means that the root appears twice in the factored form, indicating that the graph touches the x-axis at that point but does not cross it.

Front

How does the graph of a polynomial change with different leading coefficients?

Back

The leading coefficient affects the direction of the graph's end behavior; a positive leading coefficient means the graph rises to the right, while a negative one means it falls to the right.