Lecture 14: Polynomial Functions of Higher Degree & Long Division of Polynomials

_____ is a factor of the polynomial f(x).

(x-a)

A factor (x − a)^k, k > 1, yields_______ x=a of _______ k.

a repeated zero; multiplicity

A shortcut for long division of polynomials is __________, in which the divisor must be of the form x − k.

synthetic division

The _______is used to determine the left-hand and right-hand behavior of the graph of a polynomial function.

Leading Coefficient Test

The _________ Theorem states that a polynomial f(x) has a factor (x − k) if and only if f(k) = 0.

factor

A polynomial function of degree n has at most_____ real zeros and at most_____turning points.

n; n-1

The _______ Theorem states that if a polynomial f(x) is divided by x − k, then the remainder is r = f(k).

remainder

x=a is a _____of the polynomial equation f(x) = 0.

solution

When a real zero x = a, of a polynomial function f is of even multiplicity, the graph of f _____ the x-axis at x = a, and when it is of odd multiplicity, the graph of f ______ the x-axis at x = a.

touches; crosses

The graph of a polynomial function is ______, which means that the graph has no breaks, holes, or gaps.

continuous

(a, 0) is a _______of the graph of f.

x-intercept