Zeros, Multiplicity and End behavior

Front

What are the zeros of the polynomial function y = x(x - 6)(x + 5)?

Back

The zeros are 0, 6, and -5.

Front

What are the zeros of the graph with roots -4, -1, 2, and 1 with multiplicity 2?

Back

The zeros are -4, -1, 2, and 1 (multiplicity 2).

Front

How does the end behavior of a polynomial function relate to its degree and leading coefficient?

Back

The end behavior is determined by the degree and the sign of the leading coefficient.

Front

Identify the degree and leading coefficient sign for the polynomial with leading coefficient negative and degree odd.

Back

Leading Coefficient: Negative, Degree: Odd.

Front

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

Back

The roots are -2 and 7 (multiplicity 3).

Front

Which zero has an odd multiplicity among the options: -4, 4, 2, -2?

Back

The zero with an odd multiplicity is -4.

Front

Define 'zero' in the context of polynomial functions.

Back

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

Front

What is 'multiplicity' in relation to polynomial zeros?

Back

Multiplicity refers to the number of times a particular zero is repeated in a polynomial.

Front

Explain the significance of even and odd multiplicities on a graph.

Back

Even multiplicities touch the x-axis, while odd multiplicities cross the x-axis.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior is determined by the degree (even or odd) and the sign of the leading coefficient.