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Factor. $\newline$ $2g^3 + 2g^2 - 7g - 7$

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Factor by grouping

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Q. Factor.

\newline

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

Group Terms: Group terms to find common factors. $\newline$ Group the first two terms and the last two terms separately. $\newline$ $(2g^3 + 2g^2) - (7g + 7)$
Factor Common Factors: Factor out the greatest common factor from each group. $\newline$ From the first group, factor out $2g^2$ . $\newline$ $2g^2(g + 1) - (7g + 7)$ $\newline$ From the second group, factor out $-7$ . $\newline$ $2g^2(g + 1) - 7(g + 1)$
Factor Binomial Factor: Factor out the common binomial factor. $\newline$ Both groups now have a common factor of $(g + 1)$ . $\newline$ Factor out $(g + 1)$ . $\newline$ $(g + 1)(2g^2 - 7)$
Check Quadratic Factor: Check if the quadratic factor can be factored further. $\newline$ The quadratic $2g^2 - 7$ does not factor nicely with integer coefficients, so it is already in its simplest form.

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