Polynomial Functions

Front

What does multiplicity of a zero mean?

Back

How many times the zero repeats.

Front

What is the degree of the polynomial function f(x) = 2x^3 - 3x^2 + 4x - 10?

Back

3

Front

What is another way to say 'where a function crosses the x-axis'?

Back

x-intercept, zero, root, all of these.

Front

What are the roots and multiplicities of the polynomial function f(x) = 2x^3 - 3x^2 + 4x - 10?

Back

x = -1 multiplicity 2, x = 2 multiplicity 1.

Front

What is the leading coefficient of the polynomial function f(x) = 2x^3 - 3x^2 + 4x - 10?

Back

2.

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the standard form of a polynomial function?

Back

The standard form is written as f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, ordered by decreasing powers of x.

Front

What is a zero of a polynomial function?

Back

A zero of a polynomial function is a value of x for which f(x) = 0.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros, set the polynomial equal to zero and solve for x.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root.