Question

Factor completely. $x^{-4}+2 x^{-5}+x^{-6}$

   Factor completely.
$x^{-4}+2 x^{-5}+x^{-6}$

Intermediate Algebra : Concepts and Applications

Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger,… 10th Edition

Chapter 5, Problem 100

Instant Answer

Solved by Expert Ankit Gupta

07/17/2020

Step 1

Step 1: First, we rewrite the given equation $x^{-4}+2 x^{-5}+x^{-6}$ as $x^{-4}(1+2 x^{-1}+x^{-2})$ by factoring out $x^{-4}$. Show more…

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Factor completely. $x^{-4}+2 x^{-5}+x^{-6}$

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Key Concepts

Negative Exponents

This concept involves understanding that a negative exponent indicates the reciprocal of a number raised to a positive exponent. In algebra, rewriting expressions with negative exponents in their reciprocal form is a key step in simplifying and factoring expressions.

Common Factoring

Common factoring is the process of identifying and extracting the greatest common factor from an expression. In the context of expressions with exponents, this technique often involves factoring out a term with the smallest exponent, which simplifies the expression and sets the stage for further factoring.

Polynomial Factorization

This is an algebraic technique where a polynomial expression is expressed as the product of simpler polynomials or factors. Recognizing structures such as perfect square trinomials, even when they emerge from expressions with negative exponents, is crucial for complete factorization.

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