Synthetic Division: Divide Polynomials by Monomials

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Synthetic division is specifically designed for dividing polynomials by linear factors of the form x - a, where a is a known root. For divisors like ax - b or higher-degree polynomials such as x^2 - b, traditional polynomial long division is required. This method is essential for simplifying polynomials and finding roots efficiently. While synthetic division streamlines the process for specific cases, it does not apply universally to all polynomial divisions. Understanding when to use synthetic division versus long division is crucial for effective polynomial manipulation.
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so synthetic division can be used to divide polynomials by monomials. is there a to divide by
ax-b as opposed to x-b? ax^2-b? is there a general rule?
thanks.
or does one have to revert to polynomial long division.
 
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"Synthetic division" is used specifically to divide a polynomial by "x- a" for some number a. That is a very important special case since it is so often important to find all roots of a polynomial equation and dividing by x-a when a is a root you have already found reduces the equation.

Of course, you can use regular algebraic division if the divisor is something like 3x- 2 or x^2+ 4x- 3.
 

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