Factor. 7g^3 + 14g^2 - g - 2 ______

Group and Separate Terms: Group terms that can be factored by grouping. Group the first two terms and the last two terms separately. 7g^3 + 14g^2 - g - 2 = (7g^3 + 14g^2) - (g + 2)Factor Out Common Factors: Factor out the greatest common factor from each group. From the first group, factor out 7g^2. From the second group, factor out -1. (7g^3 + 14g^2) - (g + 2) = 7g^2(g + 2) - 1(g + 2)Factor by Grouping: Factor by grouping. Now that we have a common factor of (g + 2), factor it out. 7g^2(g + 2) - 1(g + 2) = (g + 2)(7g^2 - 1)Check Quadratic Factor: Check if the quadratic factor can be factored further. The quadratic factor 7g^2 - 1 is a difference of squares and can be factored further. 7g^2 - 1 = (sqrt(7)g - 1)(sqrt(7)g + 1)Write Final Factored Form: Write the final factored form. Combine the factored terms to get the final answer. (g + 2)(7g^2 - 1) = (g + 2)(sqrt(7)g - 1)(sqrt(7)g + 1)

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Algebra 2

Factor by grouping

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Q. Factor.

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7g^3 + 14g^2 - g - 2

Group and Separate Terms: Group terms that can be factored by grouping. $\newline$ Group the first two terms and the last two terms separately. $\newline$ $7g^3 + 14g^2 - g - 2 = (7g^3 + 14g^2) - (g + 2)$
Factor Out Common Factors: Factor out the greatest common factor from each group. $\newline$ From the first group, factor out $7g^2$ . From the second group, factor out $-1$ . $\newline$ $(7g^3 + 14g^2) - (g + 2) = 7g^2(g + 2) - 1(g + 2)$
Factor by Grouping: Factor by grouping. $\newline$ Now that we have a common factor of $(g + 2)$ , factor it out. $\newline$ $7g^2(g + 2) - 1(g + 2) = (g + 2)(7g^2 - 1)$
Check Quadratic Factor: Check if the quadratic factor can be factored further. $\newline$ The quadratic factor $7g^2 - 1$ is a difference of squares and can be factored further. $\newline$ $7g^2 - 1 = (\sqrt{7}g - 1)(\sqrt{7}g + 1)$
Write Final Factored Form: Write the final factored form. $\newline$ Combine the factored terms to get the final answer. $\newline$ $(g + 2)(7g^2 - 1) = (g + 2)(\sqrt{7}g - 1)(\sqrt{7}g + 1)$