PreCalc Chapter 2 Test Part 2 Flashcards Preview

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Flashcards in PreCalc Chapter 2 Test Part 2 Deck (56)
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0
Q

factor x^3+8

A

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

1
Q

how do you factor a perfect cube

A

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

2
Q

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

A

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

3
Q

is x^2 + 49 factorable?

A

yes

x-7i) (x+7i

4
Q

what is the rational zero test

A

p(constant)/q (leading coefficient

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

5
Q

what are the possible root combinations for a cubed equation

A

all real, 2 imaginary and one real

6
Q

what does lower bound say

A

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

7
Q

what is upper bound

A

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

8
Q

what is DesCartes’s Rule of signs

A

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

9
Q

what does irreducible over the reals mean

A

does not reduce into real factors

x^2-2x+10

10
Q

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

A

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

11
Q

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

A

fundamental, theorem, algebra

12
Q

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

A

linear factorization theorem

13
Q

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

A

rational zero

14
Q

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

A

conjugate

15
Q

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

A

polynomial, linear, quadratic

16
Q

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

A

irreducible, reals

17
Q

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 ________

A

Descartes’s Rule, Signs

18
Q

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

A

lower, upper

19
Q

if 5i is a zero, what else is true

A

-5i is a zero

20
Q

a set of ordered pairs

A

relation

21
Q

what is a rational function

A

fraction with polynomials

22
Q

how do you find the vertical asymptote

A

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

23
Q

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

A

y=0

it is the x-axis

24
Q

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

A

y=ratio of leading coefficients

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

25
Q

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

A

by 1: y=quotient slant asymptote

by 2: y=quotient parabolic asymptote

26
Q

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

A

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

27
Q

what is intermediate form? is it the same as undefined

A

0/0, no

28
Q

slant asymptotes and parabolic asymptotes all begin with

A

y=
so do HA
VA begins with x=

29
Q

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 ______ _______

A

rational functions

30
Q

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

A

vertical asymptote

31
Q

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

A

horizontal asymptote

32
Q

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) ________

A

slant asymptote

33
Q

do you put brackets around solutions that make the bottom 0

A

no

34
Q

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

A

flip

35
Q

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

A

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

36
Q

3 key numbers means

A

4 test regions

37
Q

key numbers are ____

A

whatever makes the top and bottom 0

38
Q

are solutions in interval notation ordered pairs

A

no

39
Q

what is the radicand

A

the polynomial under the root

40
Q

special cases are also called ______

A

unusual solution sets

41
Q

key values with solutions in the middle are called ____ points

A

border

42
Q

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

A

positive, negative

43
Q

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

A

critical/key, test intervals

44
Q

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

A

zeros, undefined values

45
Q

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

A

profit=revenue-cost

46
Q

how can you tell if an equation has 4 test regions

A

find solutions and make sure there are 3 roots

47
Q

Can you cross through a HA? VA? SA?

A

Yes no yes

48
Q

All graphs _____ the asymptotes

A

Follow

49
Q

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

A

..

50
Q

What is root 3i times root 3i

A

3i^2

-3

51
Q

Increasing and decreasing intervals use the ___ values

A

X (watch asymptotes)

51
Q

Increasing and decreasing intervals use the ___ values

A

X (watch asymptotes)

53
Q

When finding key points of rational functions ___ first

A

Simplify

54
Q

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

A

It’s down 60 going up eternally

55
Q

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

A

Yes, they are still linear