Question

Factor each expression. $$x^{4}+x^{2}-2$$

   Factor each expression.
$$x^{4}+x^{2}-2$$

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 2, Problem 98

Instant Answer

Solved by Expert Whitney Dillinger

07/17/2020

Step 1

In this case, we have a trinomial of the form $x^{4}+x^{2}-2$. Show more…

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Factor each expression. $$x^{4}+x^{2}-2$$

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Key Concepts

Difference of Squares

The difference of squares is a specific factoring method that applies when an expression can be written as the difference between two perfect squares. Using the identity a² - b² = (a - b)(a + b) simplifies the factorization process and helps in further breaking down polynomial expressions.

Polynomial Factorization

Polynomial factorization is the process of rewriting a polynomial as a product of simpler polynomials. This technique simplifies the expression and helps in solving equations by breaking a complex polynomial into factors that are easier to work with.

Substitution Technique

The substitution technique involves replacing a part of an expression with a new variable to simplify the form of the equation. This is especially useful when the polynomial has a structure that mimics a simpler form, such as a quadratic, making it easier to factor.

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