Question

Factor completely. $$ 8 x^{4}+12 x^{3}-24 x^{2} $$

Name: Problem 25, Chapter 3: Intermediate Algebra
Uploaded: 2022-02-27T14:42:02-08:00
Duration: 17 s
Channel: Erika Bustos
Description: Factor completely. 8 x^4+12 x^3-24 x^2

   Factor completely.
$$
8 x^{4}+12 x^{3}-24 x^{2}
$$

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 3, Problem 25

Instant Answer

Solved by Expert Erika Bustos

02/27/2022

Step 1

This gives us: $$ 8x^{4}+12x^{3}-24x^{2} = 4x^{2}(2x^{2}+3x-6) $$ Show more…

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Factor completely. $$ 8 x^{4}+12 x^{3}-24 x^{2} $$

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Key Concepts

Polynomial Factorization

Polynomial factorization involves rewriting a polynomial as a product of simpler polynomial factors. This transformation is crucial for solving equations, simplifying expressions, and analyzing the behavior of functions.

Quadratic Factorization and Discriminant Analysis

After removing the GCF, sometimes a quadratic factor remains. Determining the discriminant of the quadratic helps decide whether it can be factored further over the set of integers. A discriminant that is not a perfect square usually means the quadratic is irreducible over the integers.

Greatest Common Factor (GCF) Extraction

This is the process of identifying and pulling out the largest factor that is common to all terms of a polynomial. Extracting the GCF simplifies the expression and can make further factoring steps clearer and easier to carry out.

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