Find Degree of Polynomial Function

[mathdad]

Given zeros: -4, -1, 2, 3, find degree of polynomial function.

The number of zeros given indicates the degree number. True?

If so, the total degree for this polynomial function is 4.

 

[Romsek]

The number of zeros given indicates the degree number. True?

No.

\(\displaystyle (x-1)^{100}\) is degree 100 but has only a single zero at \(\displaystyle x=1\)

If all the zeros are distinct then yes, the total number of zeros is equal to the degree.

 

[Dr.Peterson]

Given zeros: -4, -1, 2, 3, find degree of polynomial function.

The number of zeros given indicates the degree number. True?

If so, the total degree for this polynomial function is 4.

A slightly clearer way to say it, that applies when there are repeated zeros, is:

• The degree of a polynomial is the sum of the multiplicities of its zeros.

In this case, if we assume the zeros all have multiplicity 1 (and in your context, it may be implied that they would have listed repeated zeros explicitly), you are correct that the degree is 4. Otherwise, we can only say that it is at least 4.