Factor. 3g^3 + 6g^2 - 8g - 16 ______

Grouping for Factoring: Group the terms into two pairs to prepare for factoring by grouping. Group the first two terms and the last two terms separately. 3g^3 + 6g^2 - 8g - 16 can be grouped as (3g^3 + 6g^2) + (-8g - 16).Factor out Common Factors: Factor out the greatest common factor from each group. From the first group (3g^3 + 6g^2), factor out 3g^2. 3g^3 + 6g^2 = 3g^2(g + 2). From the second group (-8g - 16), factor out -8. -8g - 16 = -8(g + 2).Write Factored Expression: Write the expression with the factored groups. Now we have 3g^2(g + 2) - 8(g + 2).Factor out Common Binomial: Factor out the common binomial factor (g + 2). Both terms have a common factor of (g + 2), so we can factor this out. The factored form is (g + 2)(3g^2 - 8).

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Algebra 2

Factor by grouping

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Q. Factor.

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3g^3 + 6g^2 - 8g - 16

Grouping for Factoring: Group the terms into two pairs to prepare for factoring by grouping. Group the first two terms and the last two terms separately. $3g^3 + 6g^2 - 8g - 16$ can be grouped as $(3g^3 + 6g^2) + (-8g - 16)$ .
Factor out Common Factors: Factor out the greatest common factor from each group. $\newline$ From the first group $3g^3 + 6g^2$ , factor out $3g^2$ . $\newline$ $3g^3 + 6g^2 = 3g^2(g + 2)$ . $\newline$ From the second group $-8g - 16$ , factor out $-8$ . $\newline$ $-8g - 16 = -8(g + 2)$ .
Write Factored Expression: Write the expression with the factored groups. $\newline$ Now we have $3g^2(g + 2) - 8(g + 2)$ .
Factor out Common Binomial: Factor out the common binomial factor $g + 2$ . Both terms have a common factor of $g + 2$ , so we can factor this out. The factored form is $g + 2$ $(3g^2 - 8)$ .