Factor. p^3 + 2p^2 - 8p - 16 ______

Group and Factor: Group terms to find common factors. Group the first two terms and the last two terms separately. (p^3 + 2p^2) - (8p + 16)Factor Common Terms: Factor out the greatest common factor from each group. From the first group, factor out p^2. p^2(p + 2) From the second group, factor out -8. -8(p + 2) Now we have: p^2(p + 2) - 8(p + 2)Factor Common Binomial: Factor out the common binomial factor. The common binomial factor is (p + 2). Factor (p + 2) out of the expression. (p + 2)(p^2 - 8)Recognize Difference of Squares: Recognize that p^2 - 8 is a difference of squares. p^2 - 8 can be factored as (p + √8)(p - √8). Since √8 simplifies to 2√2, we can write: (p + 2√2)(p - 2√2)Write Final Factored Form: Write the final factored form. Combine the factored parts to get the final answer. (p + 2)(p + 2√2)(p - 2√2)

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p^3 + 2p^2 - 8p - 16

Group and Factor: Group terms to find common factors. $\newline$ Group the first two terms and the last two terms separately. $\newline$ $(p^3 + 2p^2) - (8p + 16)$
Factor Common Terms: Factor out the greatest common factor from each group. $\newline$ From the first group, factor out $p^2$ . $\newline$ $p^2(p + 2)$ $\newline$ From the second group, factor out $-8$ . $\newline$ $-8(p + 2)$ $\newline$ Now we have: $\newline$ $p^2(p + 2) - 8(p + 2)$
Factor Common Binomial: Factor out the common binomial factor. $\newline$ The common binomial factor is $(p + 2)$ . $\newline$ Factor $(p + 2)$ out of the expression. $\newline$ $(p + 2)(p^2 - 8)$
Recognize Difference of Squares: Recognize that $p^2 - 8$ is a difference of squares. $\newline$ $p^2 - 8$ can be factored as $(p + \sqrt{8})(p - \sqrt{8})$ . $\newline$ Since $\sqrt{8}$ simplifies to $2\sqrt{2}$ , we can write: $\newline$ $(p + 2\sqrt{2})(p - 2\sqrt{2})$
Write Final Factored Form: Write the final factored form. $\newline$ Combine the factored parts to get the final answer. $\newline$ $(p + 2)(p + 2\sqrt{2})(p - 2\sqrt{2})$