What is the basic principle that can be used to simplify a polynomial?
Possibly these sites will be helpful. I searched Google under the key words "simplify polynomial" to get these possible sources:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut18_polyeq.htm
(Broken Link Removed)
http://www.purplemath.com/modules/polymult.htm
http://www.purplemath.com/modules/polydiv.htm
http://faculty.ed.umuc.edu/~swalsh/Math%20Articles/Polynomial.html
I hope this helps. Thanks for asking.
gori, you might have to tell us what your text defines "simplify" to mean. I may invite disagreement (not being a teacher), but there is no one, single definition of simplify. It can mean anything from canceling common factors, writing the polynomial as a product of factors, multiplying things together...and...substituting another variable(s) that transforms the polynomial to another completely different one, which is actually much easier to solve. Even if that means increasing the degree of the polynomial along the way. For now, check the text's definition and the sites given above -keeping in mind there are other meanings however.
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Unit 6 lesson 1
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what is the definition to relation, simplify fransformation and translation in math terms?
Hal is 100% correct!
To simplify a polynomial, you can use several principles and techniques depending on what you mean by "simplify." Here are some common approaches:
1. Combine like terms: In a polynomial, like terms are terms that have the same variables raised to the same powers. Combine them by adding or subtracting their coefficients.
2. Factor out common factors: Look for factors that are common to all the terms in the polynomial and factor them out. This is also known as factoring by grouping.
3. Use the distributive property: If there is a common factor between terms, you can distribute it to simplify the polynomial. This is especially useful when factoring.
4. Use the rules of exponents: When simplifying polynomials with exponents, use the rules of exponents to simplify terms with the same base.
5. Divide or multiply polynomials: If you have more complex polynomials, you may need to perform polynomial division or multiplication to simplify them. This involves long division or factoring to find the quotient or product of the polynomials.
It's important to note that the specific technique and approach to simplifying a polynomial may vary depending on the context and the specific goal you have in mind. So, it's always a good idea to refer to your textbook or the specific instructions you have to get a clear understanding of what is expected. The websites mentioned in the previous response can also provide helpful explanations and examples.