Synthetic division example 2 | Polynomial and rational functions | Algebra II | Khan Academy

Another example of applying the basic synthetic division algorithm

Missed the previous lesson?

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[timmypena]

everybody is doing online classes and my professor posted your video so we can continue our work. I'm glad she did.

[danielmak]

Wow I learned this last semester and totally forgot how to do this. Thanks for the refresher!

[erwinjedracho]

man..how did they discover this....fuck bro, this isn't math, this is

[jayoncetaylor]

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...

[reinowarren]

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)

[Sakurachan]

what if the numerical coefficient of the divisor is 2, 3 and so on not 1 . like 2x-3 instead of x-3

[Srjoemama]

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

[jayoncetaylor]

Now... where's the video explaining WHY this all makes sense?

[nii_san]

i like how he keeps the numbers colored rather than having them in just 1 boring color

[Nickadoo]

useless stuff, but i got to know it for the next math quiz! thankyou khan!

[WhatsBliss]

I actually prefer using synthetic division. I tend to make fewer mistakes and it feels like there's less to keep track of. :P

[viet-anhle]

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😂

[uggmonster]

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.

[beary]

but with the intuition he gives, that means there should be a way to divide by polynomials.

[orizbethsolis]

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?

[niloofareshghi]

is there a video with a second degree divisor?

[beary]

Can you explain the method of synthetic division with polynomials, such as (4x^3-2x^2+4)/(2x^2+5x+1)?

[gilbertmartinez]

Thanks khan academy for helping me with this now I can study in peace lol

[idsamuel]

/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 ^^

[metroid_gauntlet]

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?