Question

Factor each expression. $$ x^{4}-7 x^{2}+12 $$

   Factor each expression. 
$$
x^{4}-7 x^{2}+12
$$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 6, Problem 23

Instant Answer

Solved by Expert Charles Carter

03/11/2020

Step 1

We can treat $x^{2}$ as a single variable, say $y$. So, the expression becomes $y^{2}-7y+12$. Show more…

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Factor each expression. $$ x^{4}-7 x^{2}+12 $$

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Key Concepts

Polynomial Factorization

Polynomial factorization is the process of rewriting a polynomial as a product of lower-degree polynomials. This is a fundamental technique in algebra that simplifies expressions and aids in solving polynomial equations by finding their roots.

Substitution Method

The substitution method involves replacing a complex or higher-degree expression with a single variable to transform the problem into a simpler form. This allows one to apply standard factoring techniques, such as factoring quadratics, to expressions that originally appear more difficult.

Factoring Quadratic Equations

Factoring quadratic equations entails rewriting a quadratic expression as the product of two binomials. This approach is useful in solving or simplifying expressions, particularly when a higher degree polynomial can be reduced to a quadratic form through substitution.

Difference of Squares

The difference of squares is a specific factoring pattern applicable when an expression is the difference between two perfect squares. This method factors the expression into the product of the sum and difference of the square roots of those perfect squares, providing a straightforward simplification.

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