Question

Factor completely. $2 x^{3}+6 x^{2}-8 x-24$

   Factor completely.
$2 x^{3}+6 x^{2}-8 x-24$

Algebra and Trigonometry

Algebra and Trigonometry

Judith A. Beecher,… 4th Edition

Chapter 0, Problem 113

Instant Answer

Solved by Expert Ankit Gupta

07/04/2020

Step 1

This gives us: \[2(x^{3}+3x^{2}-4x-12)\] Show more…

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Factor completely. $2 x^{3}+6 x^{2}-8 x-24$

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Key Concepts

Polynomial Factorization

Polynomial factorization is the process of rewriting a polynomial as a product of lower degree polynomials. It involves applying techniques such as common factor extraction, grouping, and recognizing special products, making the expression easier to analyze and solve.

Difference of Squares

Recognizing a difference of squares is crucial, as it is a special pattern where an expression of the form a² - b² factors into (a - b)(a + b). This concept helps in further breaking down expressions that match this pattern after initial factors have been extracted.

Common Factor Extraction

This concept involves identifying and removing a common factor present in each term of the polynomial. Extracting the greatest common factor simplifies the expression and can reveal underlying structures that make further factorization easier.

Factoring by Grouping

This technique is used when a polynomial can be divided into groups (usually pairs of terms) that share a common factor. After factoring each group, a common binomial factor may emerge, allowing the polynomial to be expressed as a product of factors.

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