How to divide two polynomials using long division

👉 Learn how to divide polynomials by quadratic divisors using the long division algorithm. Before dividing a polynomial, it is usually important to arrange the divisor in the descending order of powers of the variable(s). To divide a polynomial by a quadratic divisor using the long division algorithm, we divide the polynomial (dividend) with the quadratic term of the divisor to get a term of the quotient. We will then multiply all the terms of the divisor by the term of the quotient and subtract the result from the dividend. The result is divided again by the quadratic term of the divisor to get another term of the quotient. This process is repeated until the quadratic term of the divisor can no longer divide into the dividend.
The result after subtracting the product of the last term of the quotient and the divisor is the remainder when the divisor divides the original polynomial. If the remainder is zero, then the divisor is a factor of the original polynomial.
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Organized Videos:
✅Divide Polynomials using Long Division
• Divide Polynomials usi...
✅Divide Polynomials using Long Division with four terms
• Divide Polynomials usi...
✅Divide Polynomials using Long Division with five terms
• Divide Polynomials usi...
✅Divide Polynomials using Long Division with missing terms
• Divide Polynomials usi...
✅Divide Polynomials using Long Division with monomial divisor
• Divide Polynomials usi...
✅Divide Polynomials using Long Division with quadratic divisor
• Divide Polynomials usi...
✅Divide Polynomials using Long Division with linear binomial divisor
• Divide Polynomials usi...
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[@brianmclogan]

you are very welcome!

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I'm a 70-year old retired engineering physicist who was NEVER exposed to this or synthetic division in school. There were times in my career it would have been useful - for integrating rational functions, say - but I always had to resort to arcane u-substitutions and the tables of integrals (Burrington, e.g.) to get there. What a godsend this would have been! It's a cold, rainy day here in New England, so I've been browsing the YT math channels, belatedly filling in holes in my education, and enjoying it immensely. Thanks for doing this!

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8 years later and your videos are still helping students, thank you!!

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happy to help you out Adrienna!

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Happy new year Mr MacLogan. This lesson filled a lot of gaps in my limited knowledge about long divisions on polynomials. What I have learned before this wasn’t enough to solve much. It just made me confused.

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[@ARM_DM]

Thank you!!! No one else had an example were they had x2 dividing into with x4

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Thank yu very mochi ありがとうございましたあなたは助かる。

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this video was super helpful, thanks! Also thanks to the students for asking good questions

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I was practicing a bonus question the teacher said would come tomorrow. And at this point, I need all the marks I can get, so thank youuu !

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great teacher! thank you so much!! but i also noticed that he didnt correct the 12 x ^2+ 3x^2= 9 x^2 answer, but i do understand that he was just teaching so its fine

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Could the remainder ever be - 4x-4/x^2+1? Or will it always be adding the remainder over the divisor

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I got the same question in my exam thank you for the help sir

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Wonderful presentation. However, I shall be obliged if a illustration is given where the divisor starts with 1 like 1--a- x2etc.

[@brianmclogan]

not sure I understand

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You are very welcome!!

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Umm.. Excuse me.. The remainder is 4x+4 because you are supposed to not put any sign when you subtract right?

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its like having 5 - (+9) = 5 - 9 = -4

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Thanks Mr. Mclogan

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Thank you sooo muchh sirr! This is really helping meee❤