Synthetic Division of Polynomials

This precalculus video tutorial provides a basic introduction into synthetic division of polynomials. You can use it to find the quotient and remainder of a division problem with polynomials.

Polynomials - Basic Operations:

Dividing Polynomials By Monomials:

How To Graph Polynomial Functions:

Intermediate Value Theorem:

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Long Division - Polynomials:

Polynomial Long Division - More Examples:

Synthetic Division of Polynomials:

Remainder Theorem & Synthetic Division:

Factor Theorem & Synthetic Division:

Rational Zero Theorem:

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Real & Imaginary Solutions - Polynomials:

Solving Polynomial Equations - Synthetic D:

Solving Polynomial Equations With Excel:

Writing Polynomial Functions Given Zeros:

Descartes Rule of Signs:

Solving Polynomial Inequalities:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

[mananite]

You're literally carrying half of my class, thank you so much

[jedthei]

For anyone (like me) who was confused about why he added a zero to the division table at 6:56: It took some time for me to figure this out too as all of the other explinations of this skipped over this part as well. But basically after playing around with a calculator for a while I figured out the pattern.

7x^3+6x-8
Basically you're counting down from the first "power of" which in this equation is x^3, so using this your next number in the equation would need to fufill x^2 and the next x^1. Since this equations skips directly to x^1 as in 6x, we need to add that placeholder 0 to fufill x^2. 6x fufils x^1 as stated above and we also need to fufill x^0 which the -8 actally does.

Another example:
4x^5+4x^2+4

Our highest "power of" in this equation is x^5 so we will be counting down from 5, the next term 4x^2 does not fufil this and since it skips both 4 and 3 we will need to add two zeros. at this point our division table should look like this:
4 0 0 4
next we need to fufil x^1 so we add another 0 and the 4 will fufill x^0 so our table should now look like this:
4 0 0 4 0 4

Hopfully this makes sense, it does to me atleast.

[BuysAboveAsk]

better explanation than my college professor

[bubonic_plague_arah]

me and my three braincells watching this 10 minutes before the test

[Lana-ordz]

I’m taking college Algebra and I love the way you teach Algebra. It’s straight to the point and easy to understand.

[mythomaniac]

You can literally explain the synthetic division of polynomials better in 2 minutes than my math teachers in the past could in an entire class period.
It finally clicked.

This channel is a godsend, just discovered it now. Wish I had it a few years back in high school.

[ihaveagunbcuzyes]

When you learn more in a 10 minute video than an hour in class

[briweenie]

Nothing better than sleeping through class and learning it at 5 am. Definetly makes more sense from you

[kingkonglee]

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[secret]

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[Mr.R_KnowsStuff]

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[mikeecarmona]

omg you are a life saver I was literally freaking out when I missed a math class and couldn't understand the notes that were given but this explained EVERYTHING .

[Dracaar]

Want you to know buddy, I am very appreciative of your videos. It isn't just the content, it's they way you make these vids; the way you teach in them. Although for the math vids, it may be easy for me to follow because I took calculus in high school. Now I'm in my freshman year and first semester of college at 26, so it has been a while and I never actually got the college credits for calculus back in high school... now I'm starting back in algebra in college :'(. (though I do have my statistics credits so that's good)
The vids I'm most appreciative of is your chemistry vids. That is my one of my intended majors and my teacher doesn't have the best lectures XD.

Much love my friend <3

[sparklingcutie]

who ever invented synthetic division must have been irritated by long division

[Rainjojo]

Since my teacher can’t teach I’m watching this 💀

[GhostLink]

"I prefer the term artificial separation, myself."

Really good stuff. Way better than my professor.

[skunkywild]

my teacher: *gives a synthetic division problem*
me: but you didn't teach me how to do this
organic chemistry tutor: *saves my butt*

[skylaralison]

I love when people explain math and make it simple.. wish everyone could do it like that

[jessejames]

These are the best math videos I have ever seen. I love how you explain every detail and point things out so we can follow

[brkspider]

Actually saved me from being behind for possibly the rest of the quarter. Thank you for explaining this better than my teacher ever could