Question

Factor out the greatest common factor. $$x^{4}+x^{3}$$

   Factor out the greatest common factor.
$$x^{4}+x^{3}$$

Prealgebra

Julie Miller, Molly… 1st Edition

Chapter 10, Problem 41

Instant Answer

Solved by Expert Liuxi Sun

07/27/2020

Step 1

In this case, the GCF is $x^{3}$ because it is the highest power of $x$ that divides both terms. Show more…

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Factor out the greatest common factor. $$x^{4}+x^{3}$$

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Key Concepts

Properties of Exponents

Understanding the rules that govern exponents is essential when factoring expressions that involve powers of a variable. The properties of exponents allow us to correctly extract common factors, by choosing the lowest exponent present in each term for a given variable, thus ensuring the proper application of the distributive property over exponents.

Polynomial Factoring

Polynomial factoring is the process of writing a polynomial as a product of its factors, which are polynomials of lower degrees. It is a fundamental algebraic technique used to simplify expressions, solve equations, and reveal important properties of the polynomial.

Greatest Common Factor (GCF)

The greatest common factor in the context of polynomial expressions is the largest expression that divides each term of the polynomial evenly. It involves identifying the highest common powers of variables and any common numerical factors among the terms, and factoring it out simplifies the expression and can lead to further factorization.

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