Question

Factor each polynomial. $x^{4}-16$

Name: Problem 61, Chapter 0: Student's Solutions Manual for College Algebra
Uploaded: 2021-05-09T22:27:34-08:00
Duration: 50 s
Channel: Erika Bustos
Description: Factor each polynomial. x^4-16

   Factor each polynomial.
$x^{4}-16$

Student's Solutions Manual for College Algebra

Margaret L. Lial,… 12th Edition

Chapter 0, Problem 61

Instant Answer

Solved by Expert Erika Bustos

05/09/2021

Step 1

A difference of squares is a term of the form $a^{2}-b^{2}$, which can be factored into $(a-b)(a+b)$. In this case, $a=x^{2}$ and $b=4$. Show more…

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Factor each polynomial. $x^{4}-16$

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Key Concepts

Polynomial Factorization

This is the process of rewriting a polynomial as a product of simpler polynomials. It is a key concept in algebra that helps in simplifying expressions, solving equations, and understanding the structure of polynomial functions.

Difference of Squares

This is a specific factoring technique used when an expression can be written in the form a² - b², which factors into (a - b)(a + b). It is a fundamental pattern used to break down and simplify polynomial expressions.

Recursive Factoring

This concept involves repeatedly applying factoring techniques such as the difference of squares to further decompose factors. It is a strategy for fully factoring polynomials into irreducible factors, ensuring that all possible simplifications are achieved.

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