Question

Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$ 6 x^{2}+54 $$

Name: Problem 79, Chapter 3: Intermediate Algebra
Uploaded: 2022-03-16T00:14:27-08:00
Duration: 8 s
Channel: Erika Bustos
Description: Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. 6 x^2+54

   Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers.
$$
6 x^{2}+54
$$

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 3, Problem 79

Instant Answer

Solved by Expert Erika Bustos

03/16/2022

Step 1

This gives us: $$ 6(x^{2}+9) $$ Show more…

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Should help you pull together all of the factoring techniques of this chapter. Factor completely each polynomial, and indicate any that are not factorable using integers. $$ 6 x^{2}+54 $$

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Key Concepts

Sum of Squares

The sum of squares refers to expressions of the form a² + b². Unlike the difference of squares, sums of squares cannot be factored over the integers. Recognizing a sum of squares is important because it indicates that the expression may be irreducible when factoring is limited to integer coefficients.

Greatest Common Factor (GCF)

The greatest common factor is the largest factor that divides each term of a polynomial. In factoring, the first step is often to extract the GCF from all terms, which simplifies the polynomial and makes further factorization techniques easier to apply.

Polynomial Factoring

Polynomial factoring involves rewriting a polynomial as a product of simpler polynomials. Techniques include factoring out the GCF, grouping, and applying special identities. The goal is to express the original polynomial as a product of factors that, when multiplied, yield the original expression.

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