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Determining Factors and Listing the Zeros of a Polynomial Using Synthetic Division

2,648 views · Published 11 October 2011 · 4:49 · Indexed 4 November 2026

Channel: Brian McLogan · 2011 · Education

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👉 Learn how to find all the zeros of a polynomial given one rational zero. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of the polynomial is zero. 

To find the zeros of a polynomial when one of the zeros is known, we use synthetic division to divide the polynomial with the given zero or we use long division to divide the polynomial with the given zero expressed in factor form. This gives the other factor of the polynomial, which can be further factored (if need be) using any of the techniques for factoring polynomials. 

After we have factored the polynomial, we can then use the zero product property to evaluate the factored polynomial and hence obtain the remaining zeros of the polynomial. Recall that the zero-product property states that when the product of two or more terms is zero, then either of the terms is equal to 0.

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Organized Videos:
✅Find all the Remaining Zeros Given a Factor or Zero
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMovC6SFRRjq93shtEvB2euC
✅Find all the Remaining Zeros Given one irrational Zero
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqbShv9dmrglfqKBwmlrMsP
✅Find all the remaining zeros given one complex zero
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoqWRf44XGASRSVAzIUYX87
✅Find all the remaining zeros given one rational zero
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMp5HfhLa40EA8ECvU7rlWAG


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