Polynomial Zeros

Front

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

Back

The end behavior will fall on both sides.

Front

How do you determine the zeros of a polynomial function?

Back

Set the polynomial equal to zero and solve for x.

Front

What does it mean for a zero to have a multiplicity greater than 1?

Back

It means that the zero is repeated that many times in the factorization of the polynomial.

Front

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

Back

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

Front

How can you express a polynomial function in factored form?

Back

By expressing it as a product of its linear factors.

Front

What are the zeros of the polynomial function f(x) = 3x(x - 4)(x + 5)?

Back

The zeros are -5, 0, and 4.

Front

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

Back

A polynomial of degree n can have up to n zeros.

Front

How do you find the multiplicity of a zero in a polynomial function?

Back

By examining the exponent of the factor associated with that zero in the factored form of the polynomial.

Front

What is the general form of a polynomial function?

Back

f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where a_n ≠ 0.

Front

What does the graph of a polynomial function look like at a zero with an odd multiplicity?

Back

The graph will cross the x-axis at that zero.