Question

Factor each expression. Assume that all variables that appear as exponents represent positive integers. $$ 2 x^{6 a}-3 x^{5 a}+7 x^{4 a} $$

Name: Problem 107, Chapter 3: Intermediate Algebra
Uploaded: 2022-02-27T16:17:24-08:00
Duration: 16 s
Channel: Erika Bustos
Description: Factor each expression. Assume that all variables that appear as exponents represent positive integers. 2 x^6 a-3 x^5 a+7 x^4 a

   Factor each expression. Assume that all variables that appear as exponents represent positive integers.
$$
2 x^{6 a}-3 x^{5 a}+7 x^{4 a}
$$

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 3, Problem 107

Instant Answer

Solved by Expert Erika Bustos

02/27/2022

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In this case, it is $x^{4a}$. Show more…

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Factor each expression. Assume that all variables that appear as exponents represent positive integers. $$ 2 x^{6 a}-3 x^{5 a}+7 x^{4 a} $$

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Key Concepts

Greatest Common Factor (GCF)

The greatest common factor is the largest expression that divides each term of the polynomial without a remainder. Identifying the GCF is a crucial step in simplifying expressions and is often the first step in the factoring process, allowing the remaining expression to be manipulated further if needed.

Properties of Exponents

Understanding the properties of exponents is essential when factoring expressions with variable exponents. These properties allow you to factor out common exponential terms by recognizing that variables with exponents can have their lowest exponent factored out as a common factor, simplifying the overall expression.

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial expression as a product of simpler expressions that, when multiplied together, give the original polynomial. This process helps simplify problems and solve equations by breaking down complex expressions into manageable factors.

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