2

Question 1

complex number

Answer 1

any number that can be written in the form a + bi
where a and b are real numbers
ex: 2 + 3i

Question 2

conjugate zero theorem

Answer 2

if P(x) a polynomial function with only real coefficients, has a + bi as a zero, then its conjugate is also a real zero

Question 3

root -k

Answer 3

i root k
where k is greater than zero

Question 4

P(x) zeros

Answer 4

if P(x) of degree n, has n zeros, then P(x) = a(x-k1)(x-k2)…(x-kn)

Question 5

multiplicity

Answer 5

the amount of times a zero occurs in a function

Question 6

Fundamental Theorem of Algebra

Answer 6

Every polynomial of degree 1 or more has at least one complex zero

Question 7

number of zeros theorem

Answer 7

polynomial of degree n has at most n distinct complex zeros

Question 8

larger multiplicities…?

Answer 8

stretch out the graph

Question 9

rational zeros theorem

Answer 9

let p(x) = classical form
if p/q is a zero of p(x), then p is a factor of a0 and q is a factor of an

Question 10

multiplicity one

Answer 10

graph crosses the x axis

Question 11

even multiplicity

Answer 11

graph bounces/turns at x axis

Question 12

odd multiplicity >1

Answer 12

graph crosses, and is tangent, at x axis

Question 13

boundness theorem (a)

Answer 13

If c > 0 and all numbers in the bottom row of the synthetic division are positive, then P(x) has no zero greater than c. The number c is called an upper bound.
*dividend has positive leading coefficient, real coefficients, and divided by x-c

Question 14

boundness theorem (b)

Answer 14

If c < 0 and the numbers in the bottom row of the synthetic division alternate in sign (with 0 considered positive or negative, as needed), then P(x) has no zero less than c. The number c is called a lower bound.
*dividend has positive leading coefficient, real coefficients, and divided by x-c