Front

What is the multiplicity of a root in a polynomial?

Back

The multiplicity of a root refers to the number of times a particular root appears in the factorization of a polynomial. For example, in the polynomial (x+1)², the root x=-1 has a multiplicity of 2.

Front

How do you find the zeros of a polynomial function?

Back

Zeros of a polynomial function can be found by factoring the polynomial, using the quadratic formula, or graphing the function to identify x-intercepts.

Front

What does it mean if a polynomial has a root with an even multiplicity?

Back

If a polynomial has a root with an even multiplicity, the graph of the polynomial will touch the x-axis at that root but will not cross it.

Front

What does it mean if a polynomial has a root with an odd multiplicity?

Back

If a polynomial has a root with an odd multiplicity, the graph of the polynomial will cross the x-axis at that root.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function of degree n has exactly n roots in the complex number system, counting multiplicities.

Front

How can you determine the number of real zeros of a polynomial?

Back

The number of real zeros can be determined by analyzing the degree of the polynomial and using Descartes' Rule of Signs, along with graphing the polynomial.

Front

What is the quadratic formula?

Back

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function. If it is positive, the graph rises to the right; if negative, it falls to the right.

Front

What is synthetic division and when is it used?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor of the form (x - c). It is quicker and easier than long division.

Front

What is a polynomial's degree?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. It indicates the maximum number of roots the polynomial can have.