Synthetic division example 2 | Polynomial and rational functions | Algebra II | Khan Academy
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- เผยแพร่เมื่อ 6 ก.พ. 2025
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Another example of applying the basic synthetic division algorithm
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everybody is doing online classes and my professor posted your video so we can continue our work. I'm glad she did.
W khan academy
Wow I learned this last semester and totally forgot how to do this. Thanks for the refresher!
don't get me wrong, you've done an awesome job explaining how synthetic division is done, I'm just looking for the specific video that you said you that you have explaining why it all makes sense...
I got your back bro just search this up "Why synthetic division works | Polynomial and rational functions | Algebra II | Khan Academy"
man..how did they discover this....fuck bro, this isn't math, this is VODOO.....
preach ... PREACH +_+=.=>_
Lol in the first video example he was like in the next example we will show you how it's like voodoo and in this video he says the same thing again😂
i like how he keeps the numbers colored rather than having them in just 1 boring color
Thank you sooo much !
Now I got it
thanks!
Sal claims that synthetic division works ONLY for x - k as a divisor, NOT SO. It also works for nx - k where the reference value is the solution to nx - k = 0, which is x = k/n.
There is a slight twist: P(x)/ (nx - k) = P(x)/[n(x - k)] = (1/n)P(x)/(x - k/n). So the quotient of P(x)/(x - k/n) must be multiplied by 1/n (or if you wish, the coefficients must be divided by n).
Try (8x³ + 2x² + 5x - 6)/(2x - 1): Using the reverence number ½ the original synthetic quotient is 8, 6, 8, with remainder -2. So the real quotient polynomial is 4x² + 3x + 4 and the remainder is -2. That is, (8x³ + 2x² + 5x - 6)/(2x - 1) = (4x² + 3x + 4) + -2/(2x - 1)
Reino Warren thanks man, it really helps
Thanks a lot! 👍
useless stuff, but i got to know it for the next math quiz! thankyou khan!
This is very helpful, Thanks! :D
in the last video he says that the degree of the divisor must be 1. In other words in the denominator you can only have (x^1)+ a number
Now... where's the video explaining WHY this all makes sense?
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@Salvador Marley Instablaster :)
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@Salvador Marley glad I could help :)
Forget this, wolfram alpha time -.-
what if the numerical coefficient of the divisor is 2,3 and so on not 1 . like 2x-3 instead of x-3
then x=3/2! Simple!!
Really helped!!! Thanks
Thanks khan academy for helping me with this now I can study in peace lol
I actually prefer using synthetic division. I tend to make fewer mistakes and it feels like there's less to keep track of. :P
but with the intuition he gives, that means there should be a way to divide by polynomials.
You did not fully explain why we change the K in x+k and can be confusing. We set x+k=0 and solve for x. This would have been easier to explain so when you tell us variables being multiplied by a number make this more complicated when it is the same proceedure.
is there a video with a second degree divisor?
How did you get the [6x to the 3rd power]? It does not make sense? I thought when you dived exponent, you are really subtracting exponents. So, How did you get 6X to the third power?
and this is why I hate math...
facts
Can you explain the method of synthetic division with polynomials, such as (4x^3-2x^2+4)/(2x^2+5x+1)?
You can't. Only works in f(x)/x-a format.
What do you do if x has a coefficient with it? Like x-3, what if you had 2x-3 instead, what would you have to do?
he said in the video that it doesn't work if it has a coefficient.
not true. it will work if it has a coefficient; you just have to divide the denominator by whatever the coefficient is to make it a coefficient of 1
It's in informal Indonesian language though haha.
By the way I've tried with more than binomials and it works! You just have to add the rows and do the same concept as in the video I gave.
I'm relieved that Indonesia still has contributions to science and math in this case, so Khan Academy can you make a video about this? I'm sure it will help people and Sukino's work can be appreciated by more people in the world.
What do you do if x has a degree with it
Synthetic division won't work, so you have to do long division.
Can you add a complex one with some thing divided by 2x-3?
and it's not impossible
Synthetic division only works with x's that have the coefficient of 1. You'd have to do long division.
no, you wouldn't. you just need to reduce the coefficient of the x term to 1 by dividing the binomial by whatever the coefficient is.
shouldn't it be minus during ring the synthetic division process rather than plus???
It's plus
so how will you be able to solve this:
14x^4+3x^3+x^2-6x+2/x^2-9x+20
that requires you to factor using synthetic division, which I learned about just recently. you need to take the factors of the constant term (plus or minus) and figure out what factors into the rest of the equation without the constant term using synthetic division. because it's a degree 4th polynomial, after you figure out what can factor into the equation, you need to factor it again using the x cubed polynomial and doing the same process as you did with the starting thing. you need to reduce it to an x squared term in order to have your whole answer, and if that x squared trinomial can factor further, then you need to factor it into its binomials.
What happens if the equation not in order by exponents
Then order them, ofc xD
/watch?v=jqXSbmKn3gs
The video is in Indonesian, but maybe you can watch the diagrams.
It's called "Horner Kino", an addition to Horner's method to divide polynomials with binomials (or more i can't be sure) found by an Indonesian mathematician Sukino. Hope it helps ^^
Is that a missing term
Where?
Why did you compare it to voodoo?
why does he separate the 487????
Iris Marchant because it's the remainder
This looks like voodoo.
Why 487/x-3？？？
Jasmine J that's what the logarithm says you separate out the last term from the answer and it is the remainder.
Wait how did 160 become + 160 and how did 17x^2 become + 17x^2??
who is the dude? I kind of want to know him.
After watching this I realised how useless my professor is.......
I understand everything except what is Voodoo?
Are you referring to Wudu in Islam?
How is this Wudu?