Polynomial Zeroes and Multiplicity

Front

What is a polynomial?

Back

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial evaluates to zero. They are also known as the roots of the polynomial.

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 x. This can involve factoring, using the quadratic formula, or other algebraic methods.

Front

What is multiplicity in relation to polynomial zeros?

Back

Front

What does it mean if a zero has an even multiplicity?

Back

If a zero has an even multiplicity, the graph of the polynomial touches the x-axis at that zero but does not cross it.

Front

What does it mean if a zero has an odd multiplicity?

Back

If a zero has an odd multiplicity, the graph of the polynomial crosses the x-axis at that zero.

Front

How do you determine the multiplicity of a zero from a polynomial function?

Back

The multiplicity of a zero can be determined by examining the factors of the polynomial. If a factor is raised to a power, that power indicates the multiplicity of the corresponding zero.

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) it has. For example, a polynomial of degree 3 can have up to 3 zeros.

Front

Write a polynomial function given its zeros: 1, -2, and 3 (all with multiplicity 1).

Back

Front

Back

The zeros of the polynomial function are -1, 4, and 5.