PreCalc Chapter 2 Test Part 2

Question 0

factor x^3+8

Answer 0

(x+2)(x^2-2x+4)

Question 1

how do you factor a perfect cube

Answer 1

in the first (), take the cubed root of both variables in the equation
in the second (), first, put in whatever you need to get the leading coefficient, then put in the opposite of the product of the first (), then whatever you need to get the constant

Question 2

is (x-1)(x^2+x+1) a product of linear factors

Answer 2

no, simplify the last trinomial by doing quadratic formula to get a product of linear factors

Question 3

is x^2 + 49 factorable?

Answer 3

yes

x-7i) (x+7i

Question 4

what is the rational zero test

Answer 4

p(constant)/q (leading coefficient

some factors of both of these things will present a zero of the equation

Question 5

what are the possible root combinations for a cubed equation

Answer 5

all real, 2 imaginary and one real

Question 6

what does lower bound say

Answer 6

you plug in a negative number and get alternating sums in return,
this will be your lowest zero

Question 7

what is upper bound

Answer 7

you plug in a higher number and get all positive sums in return
this will be your highest zero

Question 8

what is DesCartes’s Rule of signs

Answer 8

the number of positive real zeros=the number of sign variations or less than that by an even integer
the number of negative real zeros=the number of sign variations at
f(-x) or less than that by an even integer

Question 9

what does irreducible over the reals mean

Answer 9

does not reduce into real factors

x^2-2x+10

Question 10

write x^6-x^7 as a product of linear factors

Answer 10

(x)(x)(x)(x)(x)(x)(1-x)

Question 11

The _______ _______ of _______ states that if f(x) is a polynomial of degree n (n>0), then f has at least one zero in the complex number system

Answer 11

fundamental, theorem, algebra

Question 12

The _______ ________ _______ states that if f(x) is a polynomial of degree n (n>0), then f(x) has precisely n linear factors

Answer 12

linear factorization theorem

Question 13

The test that gives a list of the possible rational zeros of a polynomial function is the ______ _______ Test

Answer 13

rational zero

Question 14

If a+bi is a complex zero of a polynomial with real coefficients, then so is its ________, a-bi

Answer 14

conjugate

Question 15

Every polynomial of degree n>0 with real coefficients can be written as the product of _______ and ______ factors with real coefficients, where the ___________ factors have no real zeros

Answer 15

polynomial, linear, quadratic

Question 16

A quadratic factor that cannot be factored further as a product of linear factors containing real numbers is said to be _______ over the _______

Answer 16

irreducible, reals

Question 17

The theorem that can be used to determine the possible numbers of positive real zeros and negative real zeros of a function is called __________ __________ of ________

Answer 17

Descartes’s Rule, Signs

Question 18

A real number b is a ______ bound for the real zeros of f when no real zeros are less than b, and is a ______ bound when no real zeros are greater than b

Answer 18

lower, upper

Question 19

if 5i is a zero, what else is true

Answer 19

-5i is a zero

Question 20

a set of ordered pairs

Answer 20

relation

Question 21

what is a rational function

Answer 21

fraction with polynomials

Question 22

how do you find the vertical asymptote

Answer 22

whatever makes the denominator 0
roots of denominator
x=
be sure to factor function first as asymptotes might cancel

Question 23

how do you find the horizontal asymptote if numerator’s degree is < denominator’s degree

Answer 23

y=0

it is the x-axis

Question 24

how do you find HA if the numerator’s degree=denominator’s degree

Answer 24

y=ratio of leading coefficients

f(x)=2x-5/4-x HA:y=-2

Question 25

how do you find the HA if you numerator’s degree > denominator’s degree by 1?
by 2?

Answer 25

by 1: y=quotient slant asymptote

by 2: y=quotient parabolic asymptote

Question 26

how do you find x intercepts and y intercepts of a rational function

Answer 26

x: roots of numerator (set=0) make sure to factor first in case things cancel
y: plug 0 in for x
NOTE- be sure to write as ordered pairs, (0,0) is not a y or x intercept

Question 27

what is intermediate form? is it the same as undefined

Answer 27

0/0, no

Question 28

slant asymptotes and parabolic asymptotes all begin with

Answer 28

y=
so do HA
VA begins with x=

Question 29

functions of the form f(x)=N(x)/D(x), where N(x) and D(x) are polynomials and D(x) is not the zero polynomial are called ______ _______

Answer 29

rational functions

Question 30

when f(x)—>+/- infinity as x—>a from the left or right, x=a is a _______ ________ of the graph of f

Answer 30

vertical asymptote

Question 31

when f(x)—>b as x—>+/- infinity, y=b is a ______ ______ of the graph of f

Answer 31

horizontal asymptote

Question 32

for the rational function f(x)=N(x)/D(x), if the degree of N(x) is exactly one more than the degree of D(x), then the graph of f has a ______ (or oblique) ________

Answer 32

slant asymptote

Question 33

do you put brackets around solutions that make the bottom 0

Answer 33

no

Question 34

when you divide by a - in an inequality, ____ the sign

Answer 34

flip

Question 35

in an inequality coordinate plane graph, the shaded area are the ______ and the line indicates ________

Answer 35

values that make the equation true, value that makes the equation =

Question 36

3 key numbers means

Answer 36

4 test regions

Question 37

key numbers are ____

Answer 37

whatever makes the top and bottom 0

Question 38

are solutions in interval notation ordered pairs

Answer 38

no

Question 39

what is the radicand

Answer 39

the polynomial under the root

Question 40

special cases are also called ______

Answer 40

unusual solution sets

Question 41

key values with solutions in the middle are called ____ points

Answer 41

border

Question 42

between two consecutive zeros, a polynomial must be entirely ____ or entirely _____

Answer 42

positive, negative

Question 43

To solve a polynomial inequality, find the _______numbers of the polynomial, and use these numbers to create __________ ________ for the inequality

Answer 43

critical/key, test intervals

Question 44

the key numbers of a rational expression are its ______ and its ___ ____

Answer 44

zeros, undefined values

Question 45

the formula that relates cost, revenue, and profit is ______

Answer 45

profit=revenue-cost

Question 46

how can you tell if an equation has 4 test regions

Answer 46

find solutions and make sure there are 3 roots

Question 47

Can you cross through a HA? VA? SA?

Answer 47

Yes no yes

Question 48

All graphs _____ the asymptotes

Answer 48

Follow

Question 49

Make sure graphs don’t cross if there aren’t enough X intercepts

Answer 49

..

Question 50

What is root 3i times root 3i

Answer 50

3i^2

-3

Question 51

Increasing and decreasing intervals use the ___ values

Answer 51

X (watch asymptotes)

Question 51

Increasing and decreasing intervals use the ___ values

Answer 51

X (watch asymptotes)

Question 53

When finding key points of rational functions ___ first

Answer 53

Simplify

Question 54

Why is x^4 + x^2-60 guaranteed two real roots

Answer 54

It’s down 60 going up eternally

Question 55

Can an answer written as the product of linear factors have imaginary factors?

Answer 55

Yes, they are still linear