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