Zeros and multiplicities

Front

Back

-4 multiplicity 2, -8 multiplicity 3, 5 multiplicity 1

Front

Which root has a multiplicity of 2 in the graph?

Back

-3

Front

Back

2

Front

Back

-2 multiplicity 10, 12 multiplicity 9

Front

Write a function rule for a polynomial with zeros at -1, 2, and 7 (all multiplicity of 1).

Back

Front

Define 'zero' in the context of polynomial functions.

Back

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

Front

What does 'multiplicity' mean in relation to zeros of a polynomial?

Back

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

Front

How does the multiplicity of a zero affect the graph of a polynomial function?

Back

A zero with odd multiplicity crosses the x-axis, while a zero with even multiplicity touches the x-axis but does not cross it.

Front

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

Back

The degree of a polynomial is equal to the total number of zeros, counting multiplicities.

Front

If a polynomial has a zero at x = 3 with multiplicity 4, what does this imply about the graph at x = 3?

Back

The graph will touch the x-axis at x = 3 and will not cross it.