both long division and synthetic division utilize a repeating cycle of steps that are similar, but not exactly the same. How do the steps differ?

Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter5: Polynomials And Polynomial Functions
Section5.4: Dividing Polynomials
Problem 5.86TI: Use synthetic division to find the quotient and remainder when x49x2+2x+6 is divided by x+3 .
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 both long division and synthetic division utilize a repeating cycle of steps that are similar, but not exactly the same.  How do the steps differ?

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so how do the steps differ so like synthetic division you would only focus on the coefficient what do you focus on the long division and why is the coefficient so important in the sytheitc division if you don't mind me asking

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