Proving Equivalence of f(x) and g(x)

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SUMMARY

The discussion centers on proving the equivalence of the functions f(x) = (x-1)(x^4 + x^3 + x^2 + x + 1) and g(x) = x^5 - 1. Participants emphasize the importance of multiplying out f(x) to establish equivalence. The polynomial f(x) can be expanded to demonstrate that it simplifies to g(x), confirming their equivalence. The conversation highlights the necessity of foundational algebra skills for polynomial manipulation.

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  • Understanding polynomial multiplication
  • Familiarity with algebraic functions
  • Knowledge of algebraic identities
  • Basic skills in simplifying expressions
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  • Study polynomial multiplication techniques
  • Learn about algebraic identities and their applications
  • Practice expanding and simplifying polynomials
  • Explore the concept of function equivalence in algebra
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Students in middle to high school, educators teaching algebra, and anyone seeking to strengthen their understanding of polynomial functions and equivalence proofs.

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Consider the two functions f(x)=(x-1)(x4+x³+x²+x+1) and g(x)=x5-1. If they are equivalent, prove they are; if they are not equivalent, prove they aren't.
 
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Multiply out f(x). What do you get?

-Dan
 
topsquark said:
Multiply out f(x). What do you get?

-Dan
huh
post the steps and ans. plss
 
Can you multiply out polynomials? [math](x - 1)(x^2 + x + 1) = x(x^2 + x + 1) - (x^2 + x + 1) = x^3 + x^2 + x - x^2 - x - 1 = x^3 - 1[/math] for example.

-Dan
 
pappoelarry said:
huh
post the steps and ans. plss
Step one: take an Algebra Course!

(Where did you get this problem?)
 
pappoelarry said:
huh
post the steps and ans. plss
First step- take an eighth or nineth grade (13 or 14 year old) algebra class!
 

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