Question

Factor each expression completely. $$x^{3}+27$$

   Factor each expression completely.
$$x^{3}+27$$

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 4, Problem 106

Instant Answer

Solved by Expert Mitchell Cutler

07/07/2020

Step 1

This is because $x^{3}$ is the cube of $x$ and $27$ is the cube of $3$. Show more…

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Factor each expression completely. $$x^{3}+27$$

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Key Concepts

Sum of Cubes

In algebra, the sum of cubes is a specific pattern for factoring expressions of the form a³ + b³. The formula is a³ + b³ = (a + b)(a² - ab + b²), which allows for the expression to be broken down into a linear factor and a quadratic factor, facilitating further analysis or solving of equations.

Polynomial Factorization

Polynomial factorization is the process of expressing a polynomial as a product of simpler polynomials. It is a crucial method for simplifying expressions, solving polynomial equations, and understanding the properties of functions by reducing them into more manageable components.

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