can someone just plz tell me when i have to find a gcf in factoring
#gcf
onyx surge
quick streamBOT
somber night
do you need clarification on what the gcf is?
essentially if you have 2 number and you fully factor both of them the greatest common factor would be the biggest number that is a factor of both original numbers
so if you have 18 and 24
the factors of 18 are 1 and 18, 2 and 9, & 3 and 6
the factors of 24 are 1 and 24, 2 and 12, 3 and 8, & 4 and 6
the greatest common factor of 18 and 24 is 6 because it's the biggest number that both of them are cleanly divisible by.
if you mean in terms of factoring polynomials there really isn't any such thing as a gcf
onyx surge
i mean finding roots by factoring
somber night
ah, so if you have a polynomial like x^2 + 2x - 3 you can factor it into (x+3)(x-1), the roots are just the values of x for which the equation is 0, so for (x+3) that number is -3, and for (x-1) it's 1. the whole thing becomes 0 for x=-3, 1 because those values equate to 0(x-1) and (x+3)0 respectively.
onyx surge
i got a problem thats 2x to the power of 2 -5x = 3
somber night
like (2x^2) - 5x = 3 or (2x)^(2-5x) = 3
somber night
ok.
in that case
start by moving the 3 over to the side with the Xs
so you get 2x^2 - 5x - 3 = 0
somber night
to factor if you're gonna have something that looks like this (2x + a)(x + b)
and you have to figure out what a and b are to factor it
if you foil that you'll get 2x^2 + (a + 2b)x + ab
you have to solve for a and b so that you get a + 2b = -5 and a*b = -3
I'd start with the a*b = -3 because that tells you that one of them is negative and the other is positive
and -3 has the factors -1 and 3, & 1 and -3
try plugging those into a + 2b to figure out which should be which
onyx surge
i think i mightve typed my problem wrong i tried solving it and the factors were 1 and -6
i tried using photomath to help explain it and its not doing the problem the wrong way since i checked the answer sheet
i know how to find the gcf
but i dont know when
its kinda weird
@somber night
somber night
are you able to upload a picture of the problem
onyx surge
somber night
yeah the roots of that definitely aren't -6 and 1
onyx surge
ik
somber night
if you're ever unsure try plugging in the values
onyx surge
there the gcf results
im using x method
where u gotta find 2 numbers that add to a certain number and multiply to a certain number
somber night
where u gotta find 2 numbers that add to a certain number and multiply to a cert...
ah I get what you're saying
onyx surge
but i dont know when i gotta use x method
somber night
you found those numbers
they were -3 and 1
the reason you got -6 is because of the 2x I think
onyx surge
i have to right -5x as a difference first
oh wiat
i think i get it
if theres a 2x at the start
i got to multiply it with c
onyx surge
i came across a new huge problem
that im confused
a lot
what do u do when theres a y
@somber night
photomath cant teach me this time because it thinks im doing another type of problem
tacit heath
Is there something you can factor out from either side?
onyx surge
x?
tacit heath
Yep!
somber night
đź‘Ť
tacit heath
And so what happens if you rewrite it with x factored out?
tacit heath
y stays the same
onyx surge
so xy?
tacit heath
y = x(x^2 + 9x + 20)
onyx surge
oh
tacit heath
You didn’t multiply either side by anything
You just rearranged the way one side was written
And now you can just split x^2 + 9x + 20 up
And you’ll get something like y = x(x + a)(x + b)
So the roots are 0, -a, and -b
I’ll leave it for you to solve tho
Since I think you can do it
onyx surge
y=x(x^2+4+9x+5+20)
tacit heath
y = x(x^2 + 9x + 20)
But we already know that y = x(x^2 + 9x + 20)
tacit heath
You didn’t split it up though
You added extra numbers
You just went from
x^2 + 9x + 20
to
x^2 + 9x + 20 + 5 + 4
Clearly those can’t both be equal
tacit heath
Hold on
So the goal of factoring is to re write an expression so that all of the terms with x in them don’t have x^2
tacit heath
That is, it we have something like (x - 5)(x -4), then we know if x is 5 it becomes 0 times something or if x is 4 it becomes zero times something making the whole thing zero
tacit heath
That is, it we have something like (x - 5)(x -4), then we know if x is 5 it beco...
But if you just have x^2 - 9x + 20 (Which is equivalent) you don’t have that same information
With me so far?
onyx surge
x(x+9)
tacit heath
But taking some time to understand how it works helps too
onyx surge
alr
tacit heath
First of all do you know why distribution works?
Like how (a + b)(c + d) = ac + bc + ad + bd
Something like this might help you understand it
tacit heath
Hold on
Don’t think about this as just a formula
Really take the time to understand it
And you won’t need to “memorize where to plug it in”
tacit heath
Like how (a + b)(c + d) = ac + bc + ad + bd
When we say that these two things are equal, we mean that for every possible value that a, b, c, or d could take
So (5 + 10)(2 + 3) = 5*2 + 10*2 + 5*3 + 10*3
For example
And if you actually multiply 15 by 5
You will get the same result as adding up all of those terms
tacit heath
Like how (a + b)(c + d) = ac + bc + ad + bd
That is what we mean when we say this is true
And likewise, if you had a sequence like 5*2 + 10*2 + 5*3 + 10*3
You could rearrange it as (5 + 10)(2 + 3)
onyx surge
i cant comprehend this
tacit heath
And of course they would still be equal
tacit heath
Let me summarize:
If you have any expression in the form of
(x + a)(x + b)
It is exactly equal to
x^2 + xa + xb + ab
Which is also equal to
x^2 + x(a + b) + ab
So if you have an expression in the form of
x^2 + cx + d
And you want to write it in the form of
(x + a)(x + b) (which is still equal to x^2 + (a + b)x + c)
Then you need to find an a and b that add to c and multiply to d. Once you do, you can rewrite it as
(x + a)(x + b)
and since that is equal to
x^2 + (a + b)x + ab
and also because
a + b = c
and
ab = d (you made sure that a and b had these properties using the x method)
then
(x + a)(x + b) = x^2 + (a + b)x + ab = x^2 + cx + d
onyx surge
i dont where in the problem i put it
tacit heath
So here you have x^2 + 9x + 20
And there is a way to rewrite it
So that there is no more x^2
You have found the a and b
Where do they go?
**
**If you really don’t understand what I’ve written, I sincerely apologize, and will leave the answer to your question below, for the sake of time. I still highly encourage you to think about the way the math you are doing is working, and not just memorize “how to follow the formula”.
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you have
y = x^3 + 9x^2 + 20x
Which is equal to
y = x(x^2 + 9x + 20)
Which is equal to
y = x(x + 4)(x + 5)
And since the polynomial expression here is x(x + 4)(x + 5), and the roots of a polynomial expression are the places in which it equals zero, then the roots are x = 0, x = -4, and x = -5.
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onyx surge
alr so in y = x(x^2 +9x +20) where does 4 and 5 go
tacit heath
alr so in y = x(x^2 +9x +20) where does 4 and 5 go
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