%2Fx%5E2.jpeg "(x^6-x^5+x^4)/x^2")
Simplifying the Expression: (x^6 - x^5 + x^4) / x^2
This article explores the simplification of the algebraic expression (x^6 - x^5 + x^4) / x^2.
Understanding the Problem
The expression represents a polynomial division. We have a polynomial (x^6 - x^5 + x^4) being divided by a monomial (x^2).
The Simplification Process
To simplify, we can apply the following steps:
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Divide each term of the polynomial by the monomial:
- (x^6 / x^2) - (x^5 / x^2) + (x^4 / x^2)
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Apply the rule of exponents: a^m / a^n = a^(m-n):
- x^(6-2) - x^(5-2) + x^(4-2)
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Simplify the exponents:
- x^4 - x^3 + x^2
The Simplified Expression
Therefore, the simplified form of (x^6 - x^5 + x^4) / x^2 is x^4 - x^3 + x^2.
Conclusion
By applying basic rules of polynomial division and exponent simplification, we successfully reduced the complex expression to a simpler form. This demonstrates the importance of understanding these concepts in algebra and their application in solving mathematical problems.