multiplicity review

Front

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

Back

-2, 7 (with 7 having multiplicity 3)

Front

Which root has a multiplicity of 2?

Back

-1

Front

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

Back

x-intercept, zero, root (all of these)

Front

How many roots are shown in the picture?

Back

3

Front

Which root has even multiplicity?

Back

1

Front

Define 'multiplicity' in the context of polynomial roots.

Back

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

Front

What is the significance of a root with odd multiplicity?

Back

A root with odd multiplicity crosses the x-axis at that point.

Front

What is the significance of a root with even multiplicity?

Back

A root with even multiplicity touches the x-axis but does not cross it.

Front

How do you determine the multiplicity of a root from a polynomial equation?

Back

By factoring the polynomial and counting the number of times each root appears.

Front

What is a polynomial function?

Back

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.