#math 2
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@river plank
TheVinkler
First I want to explain something ok?
Yep
Just so you understand why we factor things
sometimes you have equation in the real world that can look something like this:
$150x^2+789x+9=123$
TheVinkler
just some random numbers ok
Yeah
@stray river I got this, we just moved to the server to have latex
Yee
Yeah I realised, just working out the factorization without intending to send
So the idea is to solve these kind of things
the idea is to able to solve $150x^2+789x-114=0$
TheVinkler
TheVinkler
The idea is that now we can solve the eqution really easly, one of these sides must be 0 and that is how we solve it ok?
So this is just the idea of factoring
Now let's get on how to do it
Continue…
TheVinkler
What I want you to do is to look at what multiplies c^2 and the constant
${\color{red}25}c^2 + 25c + {\color{blue}4}$
Youre like really good at formatting these
TheVinkler
Thank you
It's not that bad
I worked with latex for over 100 hours writing things so you get pretty good pretty fast
Ah
100?
${\color{red}25}\cdot {\color{blue}4}=100$
TheVinkler
Now is the diffucult part
${\color{red}25}c^2 + {\color{yellow}25}c + {\color{blue}4}$
TheVinkler
Okay so you want to find now 2 numbers
A and B, such that $A+B={\color{yellow}25}$ and $A\cdot B=100={\color{red}25}\cdot{\color{blue}4}$
Yeah yeah i was taught this and to make a T chart
TheVinkler
Is it okay if i add something
Sure
Okay so in order to get full marks when there is a question where a and c are perfect square numbers we are supposed to square root them
Hold on
Yes but that is just in case they are like that
Just if they are the same
${\color{green} (a+b)}{\color{green}(a+b)}={\color{green}(a+b)}^2$
TheVinkler
TheVinkler
TheVinkler
just if they are the same or like this
So back to our orignal question
${\color{red}25}c^2 + {\color{yellow}25}c + {\color{blue}4}$
TheVinkler
A and B, such that $A+B={\color{yellow}25}$ and $A\cdot B=100={\color{red}25}\cdot{\color{blue}4}$
TheVinkler
You can see that we don't have it here right?
Im sorry wdym have it ? Like no match?
Yes
Im really slow my bad
Np
Yeah
Would u like to actaully prove it's not a match?
Ye right
correct
so
Can you give me 2 numbers that sum up to 25 and multply to 100?
I am practicly asking this
Are you trying to work it out on the calculator?
Yep
It's all good
Which numbers?
20 x 5
LETS GO!
20+5
WE WINDOWS
Windows!!!
Okay so now that you find these 2 numbers you split the yellow number to the to the 2 numbers that you found
like this
$${\color{red}25}c^2 + {\color{yellow}25}c + {\color{blue}4}={\color{red}25}c^2 + 20c+5c + {\color{blue}4}$$
TheVinkler
Makes sense sor far?
Just that it makes since, the magic is yet to happen
Math has a lot of cool things with art but let's discuss that later
So now I want you to look at this and I want you to look at this as 2 speerate things to factor
${\color{red}25c^2 + 20c}+{\color{yellow}5c + 4}$
TheVinkler
Now I want you to factor the red side and tell me what you got, and the yellow side and tell me what you got
Wait what
I want you to factor the red side and then the yellow side
I thought you are american, these guys are good with seperating by color 🙂
Im canadian😭
WOAH
LMAO
XD
VINKLERR
funny I lived in Canada for 2 years
But i don’t get what to factor
Factor $25c^2+20c$
TheVinkler
Why not?
Relax let's go by it one step at a time
So first are there any type of factors between 25 and 20?
What is the common factor between 25 and 20?
TheVinkler
Now is there anything we can factor from 5c^2 and 4c?
I don’t like how it’s getting longer lol
I am writing all the steps
None right..?
Or like one
There is one thing we can factor
remeber that c is just a number
So we can factor by c
$5(5c^2+4c)=5(5c\cdot c+4c)=5c(5c+4)$
TheVinkler
Now is there anthing we can factor form 5c+4?
Correct
LET’S GO
Now can we factor anything from the yellow side?
No
Correct
:D
So after we factored everything from these 2 induvidals
we get
${\color{red}5c(5c+4)}+{\color{yellow}5c + 4}$
TheVinkler
Now do you see something intresting?
Sorry I am trying to type fast and it isn't working
Lol np
No…
Also quick random question, what two number times to -81 and adds to -36
Really bad at finding these
$5c({\color{green}5c+4})+{\color{green}5c + 4}$
TheVinkler
Are you sure that is the question?
??
Can you show me the original question? because I feel like you can simplfy it before
I took this and colored it diffrently
Oh do we do 5c(5c+4)^2?
NO
NOOO
Hell no
remember $(5c+4)^2=(5c+4)(5c+4)$
TheVinkler
$5c({\color{green}5c+4})+{\color{green}5c + 4}=(5c+1)({\color{green}5c + 4})$
Nvm i messed up
Now this is the final factored form
That confused me on so many levels
TheVinkler
How does it become 5c + 1
${\color{yellow}5c}({\color{green}5c+4})+({\color{blue}1})({\color{green}5c + 4})=({\color{yellow}5c}+{\color{blue}1})({\color{green}5c + 4})$
TheVinkler
Does this makes more sense?
And this is our final form
yep
Okay
Explained explanation 😭😭
Now the way that you write an answer like this is like that
I meant like well explanation
$25c^2 + 25c + 4=25c^2+20c+5c+4=5c(5c+4)+5c+4=(5c+1)(5c+4)$
TheVinkler
Thank you
@river plank has given 1 rep to @unborn forge
Yeah 👍
Okay try another one when you get stuck let me know, mention me so I would notice
Not sure if the teachers gonna be okay with me writing a college looking answer in a grade 10 exam
It's not college looking
I finished my questions i was doing it while you were explaining
LETS GO
Okay try this one because there is a trick
But its 12 am😭😭😭
TheVinkler
Just solve it, it isn't that bad
Two numbers that times to -6 and add to 5
Yep
6 and -1
Okay, keep going
$x^2+6x-1x-6$
𝓚𝓾𝓻𝓲
Me too
XD
So far yes
And then like
cmon u can do it!
AHHH
Split the question is two halves
Factor x^2 + 6x
And uh
1x rightttt
And the other one, x - 6 we do nothin
$(x+6)(x-6)$
No you juped
𝓚𝓾𝓻𝓲
Until here everything was correct
Mhm
TheVinkler
Lol
Oh no the -
TheVinkler
Yes
which we factor and get?
I factored -1
Yeah
$-x-6=-(x+6)$
TheVinkler
So now we factor and get?
$x(x+6)-(x+6)$
TheVinkler
Oh
Cmon you can do this
Im just confused how it became positive
the +6?
Yeah
TheVinkler
Its the same?
Yeah bevause its one
$-x-6=(-1)x+(-1)6=-1(x+6)=-(x+6)$
TheVinkler
$x(x+6)-(x+6)$ So factor this
TheVinkler
No you were saying i got this as encouragement
.
Dont you jusy gottafactor the right side?
we just did
Can you say it?
$-x-6=-(x+6)$
I might understand if its like
TheVinkler
Connected
$x(x+6)-(x+6)$
TheVinkler
So the answer is?
IS THAT NOT THE ANSWER
nope
Dudeeee rhis actually hurts
You can still factor it
By a number or just x
$x{\color{red}(x+6)}-{\color{red}(x+6)}$
TheVinkler
I need past reference 😔
$xu-u$
TheVinkler
I love tiu for dealing with me
XD np
(X - 1) ( x +6)?
Lmaooo
Yeah…