Question

Factor completely. $-98 x^{6}+196 x^{5}+8 x^{4}-16 x^{3}$

   Factor completely.
$-98 x^{6}+196 x^{5}+8 x^{4}-16 x^{3}$

College Algebra Essentials

College Algebra Essentials

Julie Miller 1st Edition

Chapter 3, Problem 6

Instant Answer

Solved by Expert Nick Johnson

08/07/2021

Step 1

This gives us: \[-2x^3(49x^3 - 98x^2 - 4x + 8)\] Show more…

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Factor completely. $-98 x^{6}+196 x^{5}+8 x^{4}-16 x^{3}$

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Key Concepts

Polynomial Factorization Techniques

Polynomial Factorization Techniques encompass a variety of methods for rewriting polynomials as a product of simpler polynomials. These methods include, but are not limited to, extraction of the GCF, factoring by grouping, and recognizing special patterns such as difference of squares, perfect square trinomials, or sum and difference of cubes. Mastery of these techniques assists in simplifying expressions to their most reduced form.

Greatest Common Factor (GCF)

The concept of the Greatest Common Factor involves identifying the largest factor, including both numerical coefficients and variable powers, that is common across all terms in a polynomial. Extracting the GCF simplifies the expression and often makes further factorization more apparent by reducing the degree or size of the remaining polynomial.

Factoring by Grouping

Factoring by Grouping is a technique used to factor polynomials with four or more terms by grouping terms in pairs or sets that have a common factor. Once common factors are extracted from each group, the resultant binomial factors are examined for commonality, which can further simplify the overall expression.

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