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Overview of dividing polynomials

2,101 views · Published 11 October 2011 · 9:14 · Indexed 31 October 2026

Channel: Brian McLogan · 2011 · Education

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👉 Learn how to divide polynomials using the long division algorithm. To be able to solve a polynomial, we need to be able to get the factors and hence the zeros. To get the factors, we use the rational zeros theorem to get one of the zeros and hence one of the factors and then divide the original polynomial with the factor obtained to get the remaining factors.
To divide a polynomial using the long division algorithm, we continuously divide the polynomial (dividend) with the term having the highest power on the variable(s) in the divisor to get the quotient. We will then multiply all the terms of the divisor by the quotient and subtract the result from the dividend. The result is divided again by the term having the highest power in the variable in the divisor to get another term of the quotient. This process is repeated until the term having the highest power of the variable in 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 from the remaining part of the dividend 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.
When a term of the original polynomial is missing, it is usually useful to replace the term with the zero value of the term for easy computation.

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Organized Videos:
✅Divide Polynomials using Long Division
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpEqXegKF4X1ZvfIfR3ZRhb
✅Divide Polynomials using Long Division with four terms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrl38sUsvo6Povp9Sgv6xzp
✅Divide Polynomials using Long Division with five terms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMo5ksA4plaC3kiz05KifyA7
✅Divide Polynomials using Long Division with missing terms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMopA0IFtxgKsp3Z5zQbjhKV
✅Divide Polynomials using Long Division with monomial divisor
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqD3NA8bc8uwMxLqwke4gpZ
✅Divide Polynomials using Long Division with quadratic divisor
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMp-Mhid4_Ow29RhmP5sOLMX
✅Divide Polynomials using Long Division with linear binomial divisor
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMp0lX4rL-EDwao_ZhVkm-Th


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