How to do Polynomial Long Division Step by Step

In this video we go through 3 examples showing you how to do Polynomial Long Division. We discuss some different strategies and techniques to make it easier.

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[tavaftw]

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[Dreamprism]

What's your opinion on a modified synthetic division for dividing a polynomial by a quadratic polynomial?

Long division by x^2 - 2x + 3 takes awhile compared to a synthetic division where we use an extra row and multiply the things in our final row by 2 and -3 to go up-and-right twice (filling out a diagonal, basically).

The method is a bit harder to learn than regular synthetic division, and it's not generally taught in books (I made it up myself but am sure others have independently come up with it before me), but if one does learn it then I believe it's faster and less error-prone than long division by quadratics.

(The method can of course be extended to division by any polynomial, but very rarely does someone need to divide by a polynomial of degree more than 2.)

[zackedge]

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[vinceescobar]

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[Bill_Wang_The_STEM_Guy]

From an algebra's POV when dealt with polynomial division is to do standard long division with polynomials, but for me having just recently taken Calculus 1, there is an epic shortcut that they call the use of the quotient rule. Please correct me if I am wrong, as I am not a certified math professor yet