Question

Which of the following represents the zeros of f(x) = 4x3 − 13x2 − 37x + 10?

what i think
x = 5
x = -2
x = 1/4

@plasmafuzer

Answer 1

these are the other answers and stuff

Answer 2

i just need reassurance like is it the right one or not

Answer 3

Yea your answers are good

Answer 4

When you finish come back to this post since it isn't as cluttered... and we will work back through the last problem.

Answer 5

perfect!! thanks, i will

Answer 6

Awesome, also may I have a medal plz :D

Answer 7

For reference: (x-4)(x+5)(x-7)

Answer 8

well deserved C:

Answer 9

Cheers :D

Answer 10

I got 100

Answer 11

CONGRATS!!!

Answer 12

Do you still want to help me with the other one? Or would you like to do it later, sorry i feel like I'm taking up your time

Answer 13

Ok now comes the real taskmaster me hehehe

Answer 14

Nope your not getting out of it that easily... Im alright Im relaxing with a keyboard on a nice Saturday

Answer 15

:p

Answer 16

perfect, okay so explain this to me please!
How did you get the answer

Answer 17

Ok so given (x-4)x distribute this for me plz

Answer 18

Ill walk you through one piece at a time and once we finish I will post a totally start to finish polished solution ok?

Answer 19

But YOU will do the work each step I will just make sure you do it right.

Answer 20

So please:
(x-4)x = ?

Answer 21

I sense uneasiness whats up?

Answer 22

Please tell me whenever you are confused.

Answer 23

okay sorry my page froze and i was trying to refresh (mess)
(x-4)x
x*4-x*x

Answer 24

correct?

Answer 25

Umm yes... except you somehow swtiched the minus sign.

Answer 26

Try it again please.

Answer 27

a(b – c) = a × b – a × c

I'm going by this,

ok lets try it again?
(x-4)x
x*x-4*x

Answer 28

There we go brilliant :D

Answer 29

yay!

Answer 30

And is there another way we can write x*x?

Answer 31

x^2?

Answer 32

BRILLIANT!!!!

Answer 33

Ok so in other words (x-4)x=x^2-4x yes? what about:
(x-4)5

Answer 34

Note the multiplication is implied in a statement written like this

Answer 35

(x-4)5

x*5-4*5

(4 has to automatically go next to the minus sign because its actually -4
thats why id messed up earlier right, i didn't catch that)

Answer 36

YES EXACTLEY :D... Now simplfy it completely

Answer 37

i.e. get rid of the * signs

Answer 38

ok, 4*5=20
but what would i do with x*5?

Answer 39

what does x*5 mean write it out in words

Answer 40

some number multiplied by five

Answer 41

is that the same as 5 times some number?

Answer 42

basically yeah

Answer 43

basically nothing that is an important point... you may not recall but way back when you were young your learnd multiplication is communicative... that means for ALL... let me say this again FOR ALL real (and later on complex) numbers a*b=b*a

Answer 44

yes thats rights, doesn't matter how you put it its still the same thing

Answer 45

so saying x*5=5*x is a fundamental point about basic arithmetic its called a field axiom... without it math wouldnt work... think about that

Answer 46

like 5*x= x*5

Answer 47

EXACTLEY :D :D

Answer 48

yeah exactly

Answer 49

(:

Answer 50

but how would i simplify this to get rid of the * and finish the equation?

Answer 51

Ok so it happens to be the convention in algebra that when you have a number times a variable (some number x) you put the number first... and you can just drop the multiplication sign.... it is implied

Answer 52

Bingo

Answer 53

5x

Answer 54

So what is (x-4)5=

Answer 55

is that it?
5x-20

Answer 56

Boooomm like you have been doing it for years :D

Answer 57

Ok lets put it together now... (x-4)(x+5)

Answer 58

really????!! that was it? i was expecting something super difficult (':

Answer 59

Everyone always does when it comes to math... it comes down to some fundamental uncertainties they have about some basic maths

Answer 60

Ill tell you my story when we finish

Answer 61

(x-4)5
x*5-4*5
x*5= 5x
4*5=20
5x-20

Answer 62

Ok what about (x-4)(x+5)???

Answer 63

Note you have basically solved it already... just in two parts...work it out step by step please and post each step as you go

Answer 64

Dont be afraid... take the leap

Answer 65

what if it was a(x+5) what would the answer be?

Answer 66

a(x+5)=?

Answer 67

@emilybbydoll Did I lose you?

Answer 68

sorry i was v hungry i had to go get a snack

Answer 69

im lost on how to
(x-4)(x+5)
i could the other one v good but idk about this

Answer 70

@plasmafuzer

Answer 71

Ok what about:
a(x+5)

Answer 72

distribute

Answer 73

Dont overthink... just do what you know you need to

Answer 74

a(x+5)

Answer 75

a(x+5)

x*a+5*a

Answer 76

Bingo... and since a is an unknown do we need the *'s?

Answer 77

yes

Answer 78

we didnt with the x's earlier... and it is just an unknown

Answer 79

so what do you think now?

Answer 80

does it matter what I call something?

Answer 81

but how would i go about it? what do i distribute first? thats what I'm confused about

Answer 82

relax dont overthink.... all we have is a(x+5) right now so lets deal with that

Answer 83

you correctly distributed it but the question was about the *'s

Answer 84

does it matter what i name a variable?

Answer 85

x(a)+5a
?
oh nvm i was talking about (x-4)(x+5)

Answer 86

we arent there yet... ok now you have parentheses... did we need them when we had x(x)?

Answer 87

you could've used it but i guess its preferable to use x^2

Answer 88

Good point... we didn't write it that was because x^2 is the BETTER way, but what about 5(x)?

Answer 89

at the end of the day x just stands in for some number and you were perfectly comfortable writing 5x yes?

Answer 90

yes

Answer 91

so if a is just standing in for something why not just ax?

Answer 92

yes... no?

Answer 93

it doesn't sound right?

Answer 94

Ok ok :) tell me why.. I just told you why it does sound right tell me why it doesnt.

Answer 95

Forget what I may or may not know.... If x is a variable that stands in for something then I can write 5x no problem you agree... but why cant I write ax is a just stands in for something... what if it was 5.. a=5 i mean

Answer 96

im guessing its informal, it just sounds like your writing something tbh

Answer 97

No not at all this is totally formal and totally allowed... my freely defining things the way that I am (as you know dont already know) is due to my ability freeing me up to be creative with the "language" that is math.