/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 40 Factor each polynomial using the... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$6 x-4 x^{2}+2 x^{3}$$

Short Answer

Expert verified
The factored form of the polynomial \(6x - 4x^{2} + 2x^{3}\) is \(2x(3 - 2x + x^{2})\).

Step by step solution

01

Identify the Greatest Common Factor

For \(6x\), \(-4x^{2}\), and \(2x^{3}\), each term has a common factor of \(2x\).
02

Factor out the Greatest Common Factor

The polynomial \(6x - 4x^{2} + 2x^{3}\) can be rewritten by factoring out the greatest common factor of \(2x\) from each term: \(2x(3 - 2x + x^{2})\).
03

Simplify the Resulting Expression

Already the polynomial is simplified; hence no further simplification is required.

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