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help-10
1e509069d0b54f3c8077dec68872ad8f
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C-H-I-T-A-N
01/17/2022 15:05:17
a and b are given but I forgot
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A Lonely Bean
01/17/2022 15:05:41
Oh, so you know the roots?
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C-H-I-T-A-N
01/17/2022 15:05:45
i.e. a parabola with a mininum
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C-H-I-T-A-N
01/17/2022 15:05:53
I do
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A Lonely Bean
7998
A Lonely Bean
false
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C-H-I-T-A-N
01/17/2022 15:06:05
This parabola is the derivative of the graph I should draw
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A Lonely Bean
01/17/2022 15:06:23
Oh
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help-10
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C-H-I-T-A-N
01/17/2022 15:06:30
So my question is: how do you draw the x-values without an x-axis
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C-H-I-T-A-N
01/17/2022 15:06:34
what is the normal way?
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help-10
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A Lonely Bean
01/17/2022 15:07:12
I guess what you can do it just draw the graph go up where the derivative is positive (the bigger the absolute value, the steeper) and go down where the derivative is negative (same thing here)
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C-H-I-T-A-N
01/17/2022 15:07:24
True
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help-10
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A Lonely Bean
01/17/2022 15:07:35
That's all I can say
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help-10
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C-H-I-T-A-N
01/17/2022 15:07:38
But do I still draw the axis?
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help-10
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A Lonely Bean
01/17/2022 15:07:46
Yeah I guess
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help-10
1e509069d0b54f3c8077dec68872ad8f
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C-H-I-T-A-N
01/17/2022 15:08:01
Because I can not say if the graph is negative or positive
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Geopchad
01/17/2022 15:09:40
what
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Geopchad
01/17/2022 15:09:42
yeah you can
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help-10
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Geopchad
01/17/2022 15:09:51
if f(x) is decreasing, then f'(x) is negative
0
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help-10
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Geopchad
01/17/2022 15:10:04
***most of the time
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help-10
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C-H-I-T-A-N
01/17/2022 15:10:05
But I only know f'(x)
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0
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help-10
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Geopchad
01/17/2022 15:10:14
ur asking
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help-10
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Geopchad
01/17/2022 15:10:17
if you can draw the graph of f(x)
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help-10
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C-H-I-T-A-N
01/17/2022 15:10:18
And need to know f(x)
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help-10
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Geopchad
01/17/2022 15:10:18
given f'(x)?
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C-H-I-T-A-N
01/17/2022 15:10:21
Yes
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Geopchad
01/17/2022 15:10:32
well there are an infinite set of solutoins
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help-10
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C-H-I-T-A-N
01/17/2022 15:10:33
So you know the shape of the graph
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help-10
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Geopchad
01/17/2022 15:10:39
all you really need to know is the shape
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C-H-I-T-A-N
01/17/2022 15:10:43
Yes
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help-10
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Geopchad
01/17/2022 15:10:44
cuz all of the graphs are just off by a constant
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help-10
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Geopchad
01/17/2022 15:10:49
so it doesn't really matter--you don't need to draw specific values of y
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help-10
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C-H-I-T-A-N
01/17/2022 15:10:50
True
1
0
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help-10
1e509069d0b54f3c8077dec68872ad8f
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C-H-I-T-A-N
01/17/2022 15:11:07
But do I still need to include a x-axis?
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help-10
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Geopchad
01/17/2022 15:11:17
yeah cuz the x's will always be the same
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help-10
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C-H-I-T-A-N
01/17/2022 15:11:20
Because I can not say if it is above or below the formula?
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help-10
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Geopchad
01/17/2022 15:11:21
the x is not dependent on the y
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help-10
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Geopchad
01/17/2022 15:11:22
the other way around
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help-10
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Geopchad
01/17/2022 15:11:29
wym by this
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C-H-I-T-A-N
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help-10
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C-H-I-T-A-N
01/17/2022 15:11:43
If I draw the x-axis so that the graph is negative
1
0
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help-10
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C-H-I-T-A-N
01/17/2022 15:11:51
That could be incorrect
1
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help-10
1e509069d0b54f3c8077dec68872ad8f
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C-H-I-T-A-N
01/17/2022 15:11:59
Because I do not know for certain that is the case
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help-10
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Geopchad
01/17/2022 15:12:00
how would you draw the x-axis so the graph is negativE?
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help-10
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Geopchad
01/17/2022 15:12:03
oh i c what u mean
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help-10
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Geopchad
01/17/2022 15:12:09
well for ur purposes it doesn't really matter
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help-10
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C-H-I-T-A-N
01/17/2022 15:12:16
I hope it doesn't
1
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help-10
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Geopchad
01/17/2022 15:12:17
you can just assume that the constant would be 0
0
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Geopchad
01/17/2022 15:12:22
for the purpose of drawing it
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help-10
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Geopchad
01/17/2022 15:12:31
and then say somewhere else that the graph could be shifted up/down any amount
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help-10
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Geopchad
01/17/2022 15:12:35
if you wanted to be really specifiuc
0
1
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help-10
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C-H-I-T-A-N
01/17/2022 15:12:37
Maybe I should add a disclaimer or paper or something
1
0
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help-10
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C-H-I-T-A-N
01/17/2022 15:12:42
To be safe
1
0
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help-10
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C-H-I-T-A-N
01/17/2022 15:12:44
Thank you
1
0
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help-10
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Geopchad
01/17/2022 15:12:49
you're welcome
0
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C-H-I-T-A-N
01/17/2022 15:12:53
.close
1
0
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help-10
4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:22:32
https://cdn.discordapp.c…4128/unknown.png
unknown.png
1
0
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help-10
4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:22:36
how to do
1
0
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help-10
4e91f38d222b494aafb3791ca1c1d900
485,903,210,272,391,200
dldh06
01/17/2022 15:23:16
Solve by factoring
0
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help-10
4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:23:24
3 x -36?
1
0
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help-10
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757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:23:31
i did that and got 108
1
0
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help-10
4e91f38d222b494aafb3791ca1c1d900
485,903,210,272,391,200
dldh06
01/17/2022 15:23:46
Is that 3 times -36?
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help-10
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BlzrdStrike
01/17/2022 15:23:54
then i didnt know what number multiplied to get -108 and adds to get -3
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help-10
4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:23:57
yes
1
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485,903,210,272,391,200
dldh06
2659
dldh06
false
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Geopchad
01/17/2022 15:24:24
you should first (to make it easier) divide everything by 3
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1
757,301,836,687,605,900
BlzrdStrike
7826
BlzrdStrike
false
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Geopchad
01/17/2022 15:24:26
to get:
0
1
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help-10
4e91f38d222b494aafb3791ca1c1d900
328,662,734,008,746,000
Geopchad
01/17/2022 15:24:32
$x^2-x-12 = 0$
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1
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help-10
4e91f38d222b494aafb3791ca1c1d900
510,789,298,321,096,700
TeXit
01/17/2022 15:24:34
**Yottachad**
https://cdn.discordapp.c…734008745984.png
328662734008745984.png
0
1
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help-10
4e91f38d222b494aafb3791ca1c1d900
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Geopchad
01/17/2022 15:24:42
and this is much easier to factor than the last one
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4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:24:49
mhm
1
0
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help-10
4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:25:02
and what if the number werent divisible by the leading coeffecient
1
0
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help-10
4e91f38d222b494aafb3791ca1c1d900
485,903,210,272,391,200
dldh06
01/17/2022 15:25:19
Then you can do the method you were doing
0
1
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4e91f38d222b494aafb3791ca1c1d900
328,662,734,008,746,000
Geopchad
01/17/2022 15:25:22
yep
0
1
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help-10
4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:25:22
ok
1
0
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help-10
4e91f38d222b494aafb3791ca1c1d900
485,903,210,272,391,200
dldh06
01/17/2022 15:25:26
Or quadratic formula
0
1
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help-10
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328,662,734,008,746,000
Geopchad
01/17/2022 15:25:35
$(3x+a)(x+b) = 0$
0
1
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help-10
4e91f38d222b494aafb3791ca1c1d900
510,789,298,321,096,700
TeXit
01/17/2022 15:25:37
**Yottachad**
https://cdn.discordapp.c…734008745984.png
328662734008745984.png
0
1
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
328,662,734,008,746,000
Geopchad
01/17/2022 15:25:38
then you would try to find a and b
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1
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BlzrdStrike
01/17/2022 15:25:58
how
1
0
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help-10
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757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:26:02
zpp?
1
0
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help-10
4e91f38d222b494aafb3791ca1c1d900
328,662,734,008,746,000
Geopchad
01/17/2022 15:26:13
mayb
0
1
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help-10
4e91f38d222b494aafb3791ca1c1d900
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dldh06
01/17/2022 15:26:30
Fyi factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 and 108
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4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:26:48
wait how did u get this
1
0
510,789,298,321,096,700
TeXit
0796
TeXit
true
122
help-10
4e91f38d222b494aafb3791ca1c1d900
485,903,210,272,391,200
dldh06
01/17/2022 15:27:04
(1, 108), (2, 53), (3, 36), so on
0
1
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null
null
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122
help-10
4e91f38d222b494aafb3791ca1c1d900
485,903,210,272,391,200
dldh06
01/17/2022 15:28:10
That's the general form because you know if there was no leading coefficient, the form is $(x + a)(x + b) = 0$
0
1
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null
null
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122
help-10
4e91f38d222b494aafb3791ca1c1d900
510,789,298,321,096,700
TeXit
01/17/2022 15:28:12
**dldh06**
https://cdn.discordapp.c…210272391178.png
485903210272391178.png
0
1
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null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
485,903,210,272,391,200
dldh06
01/17/2022 15:28:37
But there is a coefficient of 3, meaning that when you FOIL, there has to be a 3x
0
1
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:28:50
ok
1
0
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
485,903,210,272,391,200
dldh06
01/17/2022 15:29:03
To obtain 3x^2
0
1
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:29:38
so where are we so far
1
0
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
485,903,210,272,391,200
dldh06
01/17/2022 15:30:20
You just factor $x^2-x-12 = 0$
0
1
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
510,789,298,321,096,700
TeXit
01/17/2022 15:30:22
**dldh06**
https://cdn.discordapp.c…210272391178.png
485903210272391178.png
0
1
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:31:15
$(x + 1) (x - 11)?$
1
0
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
510,789,298,321,096,700
TeXit
01/17/2022 15:31:17
**BlzrdStrike**
https://cdn.discordapp.c…836687605850.png
757301836687605850.png
0
1
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
485,903,210,272,391,200
dldh06
01/17/2022 15:31:44
No
0
1
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:31:54
then what is it
1
0
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
485,903,210,272,391,200
dldh06
01/17/2022 15:32:23
Does -11 * 1 equal 12? And does it add up to -1?
0
1
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:32:46
$(x - 1) (x + 11)??$
1
0
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
510,789,298,321,096,700
TeXit
01/17/2022 15:32:58
**BlzrdStrike**
https://cdn.discordapp.c…836687605850.png
757301836687605850.png
0
1
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:33:00
wait
1
0
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
485,903,210,272,391,200
dldh06
01/17/2022 15:33:29
If you FOIL, does the math check out, to make $x^2-x-12 = 0$?
0
1
null
null
null
null
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122
help-10
4e91f38d222b494aafb3791ca1c1d900
510,789,298,321,096,700
TeXit
01/17/2022 15:33:32
**dldh06**
https://cdn.discordapp.c…210272391178.png
485903210272391178.png
0
1
null
null
null
null
null
122
help-10
4e91f38d222b494aafb3791ca1c1d900
757,301,836,687,605,900
BlzrdStrike
01/17/2022 15:33:33
$(x - 1) (x + 12)$
1
0
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