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

Demonstrating why synthetic division gives you the same result as traditional algebraic long division

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[celestialorb]

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.

[vijaykumare]

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

[Saltydogg]

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

[glennrickelton]

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-iihg]

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

[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!

[adityamishra]

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

[matthewschechla]

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

[bozopapi]

I am Addicted to this Mans voice very nice helpful

[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 ...😊

[GZuZ]

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 YouTube 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.

[kristenyang]

magic...thanks a lot, it really helps

[lub]

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?

[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-ddxo]

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

[AmbiambiSinistrous]

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

[Connor-khsh]

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

[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.

[minakshianandphalke]

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