Math 185 Exam 2 Topics
Exam 2 will cover Sections 3.1 through 3.6
State the following definitions
Polynomial of degree n
Complex number
Real part of a complex number
Imaginary part of a complex number
Vertical asymptote
Horizontal asymptote
State the following theorems
Intermediate value theorem for polynomials
The Division Algorithm
Factor Theorem
Fundamental theorem of algebra
Be able to do the following
Evaluate the end behavior of polynomials
Graph polynomial functions by hand
Apply the theorem on local extrema of polynomials (pg 268)
to determine the minimum possible degree of a polynomial
with a given graph
Identify local extreme points and local extreme values of
polynomial functions
Solve a “box” problem like 76 or 77 from Section 3.1
Solve long division and synthetic division problems with polynomials
Apply the remainder theorem to evaluate P(x) at x = c using synthetic
division
Find a polynomial with specified zeros
Apply the rational zeros theorem to list all possible rational
zeros of a given polynomial with integer coefficients
Find all rational zeros of a polynomial
Completely factor a polynomial into linear and quadratic factors
Completely factor a polynomial into linear factors using complex numbers
Determine possible numbers of real zeros of a polynomial using
DesCartes’ rule of signs
Recognize an upper or lower bound for the real zeros of a polynomial using
the upper and lower bounds theorem
Use the quadratic formula to find zeros of a quadratic polynomial
Find the zeros of a polynomial function using a graphing utility
Solve problems like 83-88 of Section 3.3
Perform arithmetic on complex numbers, to include addition, subtraction,
multiplication, division, and finding the complex conjugate
Calculate the square root of a negative number
Determine the multiplicity of a zero of a polynomial by factoring
Find the horizontal, vertical, and/or slant asymptotes of a rational function
Graph a rational function by hand or using a graphing utility
Solve problems like 67-71 in Section 3.6