Frequently Asked Questions
When can I use synthetic division?
Only when dividing by a linear factor of the form (x minus r). For higher-degree divisors, use polynomial long division.
What is the remainder theorem?
Dividing p(x) by (x minus r) gives a remainder equal to p(r). Synthetic division therefore is also the fastest way to evaluate a polynomial at a point.
How is it used in finding roots?
If a rational root candidate gives remainder zero, it is a root. Synthetic division then yields a depressed polynomial of degree one lower, which you keep factoring.
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