Factor the following polynomial
3x^{3}+5x^{2}+x-1
#Trinomial
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rugged widgetBOT
Factor the following polynomial
3x^{3}+5x^{2}+x-1
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distant drum
Factor the following polynomial
3x^{3}+5x^{2}+x-1
use rational root theorem
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use rational root theorem
The wikipedia page looks out of my league
can you demonstrate this by solving it line by line
it sounds tedious but I learn it the best in such a way
I factored it to (x)(x-(1/3))(x+1) - 7 = 0
Which Is most likely incorrect
distant drum
can you demonstrate this by solving it line by line
basically (wikipedia overcomplicates things) use the leading term's coefficient's factors
and the constant term's factors
and do this
$\pm{\frac{\text{factors of leading term coefficient}}{\text{factors of constant}}$
crystal scarabBOT
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Compile Error! Click the 
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(You may edit your message to recompile.)
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3x^3 + 2x^2 + x -7
x(3x^2 + 2x + 1) - 7 = 0
(x)(x-(1/3))(x+1) - 7 = 0
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**;( \| 追放された興奮**
Compile Error! Click the <:errors:504266556054962196> reaction...
If you can tell, what are the factors of the leading term coefficient and the factors of the constant
How can it be +/ if there are 3 solutions
distant drum
How can it be +/ if there are 3 solutions
no, these are possible solutions
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so x +/ (3-7)
(x+ 3-/7)( x - (3/-7)(x+?)
@distant drum If I could start over
wait nvm i wont
@distant drum Wait
Should I just factor out the x to like (x)(quadratic) and then for the quadratic part use the formula?
to get the other factors
so for a new equation x^3 + 7x^2 + x = 0 I got
(x)(x+(7/2)-((3sqrt5)/2))(x+(7/2)+((3sqrt5)/2)
distant drum
<@1245133657690214403> If I could start over
what???
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nvm
distant drum
nonononoonoo
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i dont need to satrt over
distant drum
here, i need to explain it better
for this example, the possible rational roots would be:
$\frac{[-1,1]}{[1,3]}$
crystal scarabBOT
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distant drum
for which equation
original equation divided by x+1
distant drum
and what does that solve for again
it allows you to get the other roots
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Alr
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@distant drum I finaly understand how zero product property is used in these equations
distant drum
<@1245133657690214403> I finaly understand how zero product property is used in ...
👍
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any one of the boxes (x-a) needs to = 0 for it to be a "zero value"
as ill call it here'
distant drum
yep
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so I factores 5x^3 + 8x^2 +3x + 2 = 0 into
(x^2)(5x+8)(3x+2)
so then x = -8/5
x = 0
x= -2/3
genius!
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😭
(5x^3 + 8x^2) + 3x+2
(x^2)(5x+8) + 3x+2
Oh wait
fuck!!
@distant drum How do I get rid of the d value of these polynomials which arent multiplied
im always left with a stickler
(x^2)(5x+8) + (3x+2)
distant drum
<@1245133657690214403> How do I get rid of the *d* value of these polynomials wh...
use rational root theorem for polynomials above degree 2
no factoring cubic
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for this example, the possible rational roots would be:
I dont know what the "possible rational roots" are
Oh there is no solution for this particular equation
@distant drum Do you take
The leading coefficient
distant drum
yes
distant drum
no
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distant drum
$a_0$ is the constant term
crystal scarabBOT
;( | 追放された興奮
distant drum
what the hell
that is an aboslutely horrendous example for a rational root theorem problem
distant drum
Idk how to interperet subscripts
dw about it
distant drum
so do i divide
so it is $\pm\frac{\text{factors of} a_0}{\text{factors of} a_n}$, where $a_0$ is the constant term of the polynomial and $a_n$ is the leading coefficient
crystal scarabBOT
;( | 追放された興奮
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there is no constant in x^3 + 5x^2
there are no factors
what does that mean
@distant drum ❗
distant drum
there is no constant in x^3 + 5x^2
no it just means that 0/factors are the rational roots
which is obviously 0
i gotta eat give me a few mins
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Also, wait, this works perfectly
x^3 + 5x^2 = 0
x^2(x+5)
(x^2) = 0 x = 0
x+5= 0 x = -5
distant drum
Also, wait, this works perfectly
x^3 + 5x^2 = 0
x^2(x+5)
👍
you just gotta notice when and when not to use RRT
and if anything is factorable
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Do you know 1 equation I can practice using rrt with
Also, one more thing
for x^3 + 5x^2 3x - 1 = 0 I got
(x+1)(x^2-4x-1)
Can you just move the 1 like that into a convenient place?
same with
2x^3 5x^2 + 3x -3
x(2x^2 + 5x +3) -3
(x-3)(2x^2 +5x+3)
distant drum
same with
2x^3 5x^2 + 3x -3
x(2x^2 + 5x +3) -3
(x-3)(2x^2 +5x+3)
nope that isn’t correct
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x^3-6x^2+11x-6
Divisors of 6 = 2,3,1
(2,3,1)/(1)
1 = leading coefficient
the rational roots are 2 3 1
Yikes I couldnt be more far off
+-2, +-3, +-1/+-1
None of these work
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@distant drum Shall we continue
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what do I do again
As in
if there are multiple terms on the b ottom do I div ide each term on the top by one term on them bottom and then the other term
so I have twice as many solutions as I do on the top
distant drum
if there are multiple terms on the b ottom do I div ide each term on the top by ...
in this case, there aren't multiple terms on the bottom
but yes, your reasoning is correct
so it is like a matching game, if you get what i mean.
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so if it ws
(20,40,18,6,8,)/(4,2,6,4) it would be
20/4 20/2 20/6 20/4
40/4 40/2 40/6
18/4
You get what I mean
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seems time consuming
Hahahahaha
Wait there is only 1 constant
is it the
Factors of the leading coefficient'
divided by factors of the constant
correct?
distant drum
Factors of the leading coefficient'
other way around
distant drum
yes
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awesome
distant drum
👍
distant drum
and this will of course become tedious
yes but you gotta do what you gotta do 
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yes but you gotta do what you gotta do <:3am:1165966497177407621>
is there an algorithim on the ti 84 for this
distant drum
no
you could technically create one but i dont think it can calculate factors with a single function
you have to create a whole seperate program for that
distant drum
any power or
any power
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alr
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