Question

Factor completely. $5 x^{2}+35 x+30$

   Factor completely.
 $5 x^{2}+35 x+30$

Elementary Algebra

Elementary Algebra

Lynn Marecek 2nd Edition

Chapter 7, Problem 139

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Solved by Expert Edward Downes

07/14/2021

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The GCF here is 5. Show more…

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Factor completely. $5 x^{2}+35 x+30$

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Key Concepts

Distributive Property

The distributive property is a fundamental algebraic principle used in factoring. It allows an expression to be rewritten as a product of factors by distributing a common factor across terms, which is crucial both in extracting the GCF and in rewriting polynomials in factored form.

Greatest Common Factor (GCF) Extraction

This concept involves identifying and removing the largest factor that is common to all terms in a polynomial. Extracting the GCF simplifies the expression and often makes other factoring methods more evident.

Factoring Quadratic Polynomials

This method specifically applies to quadratic expressions of the form ax² + bx + c. The technique typically involves finding two numbers that multiply to a·c and add to b, allowing the quadratic to be rewritten as a product of two binomials.

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