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

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## how do you factor a perfect cube

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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

1

## factor x^3+8

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

2

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

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

3

## is x^2 + 49 factorable?

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yes

(x-7i) (x+7i)

4

## what is the rational zero test

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p(constant)/q (leading coefficient

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

5

## what are the possible root combinations for a cubed equation

### all real, 2 imaginary and one real

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## what does lower bound say

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you plug in a negative number and get alternating sums in return,

this will be your lowest zero

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## what is upper bound

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you plug in a higher number and get all positive sums in return

this will be your highest zero

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## what is DesCartes's Rule of signs

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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

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## what does irreducible over the reals mean

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does not reduce into real factors

x^2-2x+10

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

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

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## 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

### fundamental, theorem, algebra

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

### linear factorization theorem

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

### rational zero

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

### conjugate

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## 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

### polynomial, linear, quadratic

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

### irreducible, reals

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## 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 ________

### Descartes's Rule, Signs

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## 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

### lower, upper

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## if 5i is a zero, what else is true

### -5i is a zero

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## a set of ordered pairs

### relation

21

## what is a rational function

### fraction with polynomials

22

## how do you find the vertical asymptote

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whatever makes the denominator 0

roots of denominator

x=

be sure to factor function first as asymptotes might cancel

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

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y=0

it is the x-axis

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

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y=ratio of leading coefficients

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

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##
how do you find the HA if you numerator's degree > denominator's degree by 1?

by 2?

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by 1: y=quotient slant asymptote

by 2: y=quotient parabolic asymptote

26

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

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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

## what is intermediate form? is it the same as undefined

### 0/0, no

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## slant asymptotes and parabolic asymptotes all begin with

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y=

so do HA

VA begins with x=

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