Factor the expression completely. 6x^(3)-x Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression 6x^3 - x. The terms 6x^3 and -x both have a common factor of x.Factor out GCF: Factor out the GCF from the expression. 6x^3 - x = x(6x^2 - 1)Check for further factorization: Check if the remaining expression inside the parentheses can be factored further. The expression 6x^2 - 1 is a difference of squares since it can be written as (sqrt(6)x)^2 - 1^2.Factor difference of squares: Factor the difference of squares using the identity a^2 - b^2 = (a + b)(a - b). 6x^2 - 1 = (sqrt(6)x + 1)(sqrt(6)x - 1)Write final factored form: Write the final factored form of the original expression by combining the GCF factored out in Step 2 with the factored form from Step 4. 6x^3 - x = x(sqrt(6)x + 1)(sqrt(6)x - 1)

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Factor the expression completely.

6x^(3)-x
Answer:

Factor the expression completely. $\newline$ $6 x^{3}-x$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Factor the expression completely.

\newline

6 x^{3}-x

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Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression $6x^3 - x$ . The terms $6x^3$ and $-x$ both have a common factor of $x$ .
Factor out GCF: Factor out the GCF from the expression. $\newline$ $6x^3 - x = x(6x^2 - 1)$
Check for further factorization: Check if the remaining expression inside the parentheses can be factored further. $\newline$ The expression $6x^2 - 1$ is a difference of squares since it can be written as $(\sqrt{6}x)^2 - 1^2$ .
Factor difference of squares: Factor the difference of squares using the identity $a^2 - b^2 = (a + b)(a - b)$ . $\newline$ $6x^2 - 1 = (\sqrt{6}x + 1)(\sqrt{6}x - 1)$
Write final factored form: Write the final factored form of the original expression by combining the GCF factored out in Step $2$ with the factored form from Step $4$ . $\newline$ $6x^3 - x = x(\sqrt{6}x + 1)(\sqrt{6}x - 1)$