Zeros, Multiplicities, and Degrees of Polynomials

Front

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

Back

The roots are -2 and 7 with multiplicity 3.

Front

What is the polynomial with 3 factors of (x – 1) and 2 factors of (x + 7)?

Back

b(x) = (x - 1)^3 (x + 7)^2

Front

What is the equation of a polynomial with 5 factors of (x – 5), 6 factors of (x + 5), and 4 factors of (x + 4)?

Back

f(x) = (x - 5)^5 (x + 5)^6 (x + 4)^4

Front

Define a root of a polynomial.

Back

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

Front

What is multiplicity in the context of polynomial roots?

Back

Multiplicity refers to the number of times a particular root appears in a polynomial.

Front

How does the multiplicity of a root affect the graph of a polynomial?

Back

If a root has an odd multiplicity, the graph crosses the x-axis at that root. If it has an even multiplicity, the graph touches the x-axis but does not cross it.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

How do you determine the degree of a polynomial given its factors?

Back

The degree is the sum of the multiplicities of all the factors.

Front

What is the relationship between the roots and the factors of a polynomial?

Back

Each root corresponds to a factor of the polynomial in the form (x - root).

Front

If a polynomial has a degree of 4, what is the maximum number of roots it can have?

Back

A polynomial of degree 4 can have a maximum of 4 roots.