Why synthetic division works | Polynomial and rational functions | Algebra II | Khan Academy

[@celestialorb1680]

I often am not comfortable with using methods that I don't understand how they solve. This video was brilliant in helping me understand synthetic division and its properties as now Ill be able to use it in most functions without the grueling process of long division.

[@vijaykumare3454]

Thanks a lot ... damn helpful for those whose school classes don't move well ... got a good clarity

[@glennrickelton4093]

Brilliant explanation - other videos show how algebraic division and synthetic division work but none show the connection between WHY they are connected...WELL DONE!

[@Ash-ii4hg]

I know this video is 8 years old but it’s so helpful. Thank you Sal!

[@Saltydogg909]

Bravo Sal.., thank you to the 10th power

[@Dremple]

Nobel Peace Prize have been handed out for much less...you SERIOUSLY Deserve one for all of the People you have actually HELPED improve their(ME)life's. Thanks!

[@monoman4083]

Good to see how things work..

[@bozopapi]

I am Addicted to this Mans voice ........... very nice explanation.............very helpful

[@adityamishra1038]

all the misunderstanting is now clear. wow it's really wonderful to learn every maths problem to you sal.

[@chaneysullivan4263]

hey, it finally makes sense!

[@umrkhayam]

Thanks a bunch ! It actually made things easier ! But can you try explaining it again I mean I get how we can drop down the first one ... But can you tell me about the others ...😊

[@evasmerekanych7894]

Makes it so much clearer

[@GZuZ2012]

Thanks for this video. I always got in trouble for doing all the math in my head. I would then have to explain how I was able to get the answers. The school put me in a math competition and in grade 4 I was at a grade 8 level and I didn't study ever. I stayed away from mathematics the rest of my life because I was sick of having to explain why my way worked and I lost confidence in it working until I started to view some of your videos.

[@tom_something]

Thanks for this explanation! I was watching some shorts on KZbin or Facebook earlier today and the topic of "synthetic division" came up. I studied up through AP calculus in high school, and I don't think synthetic division was ever a thing in my entire high school math studies. The phrase sounded completely foreign to me. I do realize synthetic division is algebra and not calculus, but all roads lead to AP tests, so I think the reason it was never part of the curriculum in my algebra studies was because even algebra was preparing me for pre-calc and then AP calculus so I could get a good score on the AP calculus test three years later. Anyway, it's Sunday and I like to cut loose on the weekend, so I decided to Google some practice problems so I could try out the process and check my results. I didn't get 100%. Sloppy arithmetic. I'm rusty, but I've always been sloppy, too. Anyway, I did learn today 1) what it's for and 2) how to do it. But I'll forget how to do it if I don't also learn _why_ it works. That's one of the things I always liked about my math classes: everything builds on stuff we learned previously, and then something builds on that. As long as you have a good understanding of why the previous thing works, you've got a solid foundation for understanding the next thing that comes out of it. It's like monkey bars. So again, thank you for this.

[@michaelangu112]

intense math

[@lub094]

I'm doing something very similar - the Horner scheme, but I need to know, how to choose the number after the x (for example here it's -4), so the remainder is 0?

[@kristenyang9546]

magic...thanks a lot, it really helps

[@matthewschechla6964]

khan Academy is the only reason I'm surviving my math class right now

[@Connor-kh8sh]

Do I put a 0 in if I'm missing a constant?

[@user-yn2bd7gs4j]

yes

[@Orphen01]

Maybe a video about sound synthesis?

[@KendrickSajorda]

why do you turn (x+4) into the negative -4 when you do the synthetic division?

[@user-yn2bd7gs4j]

because it must be in the form x-c so to make x+4 into x-c form it is essentially just saying x- -4 i hope that makes sense

[@MC-mx1mt]

So that you dont need to keep remembering to subtract like in long division. When you negative that constant, you can now add instead of subtracting, since subtracting is a bit more tedious than adding

[@susantkumarparida1712]

We subtract in division. So it makes sense to multiply negative and add it.however u can just keep it positive and subtract.

[@justintimetoclashandbrawl3348]

x+4 = 0, x = -4

[@AmbiambiSinistrous]

:'D Was just wondering how synthetic division worked a few weeks ago. Thank you!

[@乐易盎]

Great Video!

[@frankiedelacruz5787]

when do you know if you have a remainder?

[@user-yn2bd7gs4j]

when the last addition does not add to 0

[@Riayza]

Khan saved me once again

[@bolinvel1676]

thank u soo much

[@CanoManuelGonzaga]

It has limitations though because you can't divide when the divisor has two different variables such as x + y. Long division is still necessary.

[@uzairhussain4856]

synthetic division is a shortcut form long division for the special case as explained.

[@carrissahenry]

How do you know what is a remainder and what isn't?

[@user-yn2bd7gs4j]

the remainder is after the 1st degree term

[@danbrennan1880]

The remainder is after the 0 degree term

[@IaKhanic]

first, thnx sal for helping me, great video

[@gtrslayer1]

Sal... i looooove you!!!

[@ahmedkh1900]

that was excellent

[@natominister5191]

What would happen if the x in (x+4) had a coefficient

[@Hi_Brien]

Wow, I forgot how to do long division... I learned that like 7 years ago... that's sad. I haven't USED it in 5 years. Then fractions became easier to use than division, then calculators became my main form of calculating.

[@PranavKumar-dd2xo]

I didn’t understand why did u write the remainder -121 as -121/ (x-4)

[@carman9457]

i thought you where supposed to add it not subtract?

[@BhaswataChoudhury-e2e]

this is traditional division algorithm. where we subtract it and not add

[@deltanebula8622]

do you do all of this with a mouse?

[@minakshianandphalke98]

everyone explains how to use a washing machine but nobody explain how does it actually,basically works!!!!!! hope you understand what I mean...

[@lunaalhayya8700]

Big like

[@6194432026]

THANKS BRO. I KNOW YOU'RE ALL BIG SHOT NOW WITH BILL GATES'S HELP, BUT THANKS FOR STILL PERSONALLY MAKING VIDEOS!!!

[@wilfredochavarria5015]

thank you alibaba420

[@Kevin-p2l5b]

Okay

[@LordZelgadis1]

this is amazing