Factor. 5s^3 + 10s^2 - s - 2 ______

Group Terms: Group terms to make factoring easier. We can group the terms as follows: (5s^3 + 10s^2) and (-s - 2).Factor Common Factor: Factor out the greatest common factor from each group. From the first group (5s^3 + 10s^2), we can factor out 5s^2, which gives us 5s^2(s + 2). From the second group (-s - 2), we can factor out -1, which gives us -1(s + 2).Write Factored Expression: Write the expression with the factored groups. Now we have 5s^2(s + 2) - 1(s + 2).Factor Common Binomial: Factor out the common binomial factor. We can see that (s + 2) is a common factor in both terms, so we factor it out to get (s + 2)(5s^2 - 1).Factor Difference of Squares: Factor the difference of squares if possible. The term 5s^2 - 1 is a difference of squares, as it can be written as (√5s)^2 - 1^2. We can factor this as (5s^2 - 1) = (√5s + 1)(√5s - 1).Write Final Form: Write the final factored form. The fully factored form of the polynomial is (s + 2)(√5s + 1)(√5s - 1).

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Q. Factor.

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5s^3 + 10s^2 - s - 2

Group Terms: Group terms to make factoring easier. $\newline$ We can group the terms as follows: $5s^3 + 10s^2$ and $-s - 2$ .
Factor Common Factor: Factor out the greatest common factor from each group. $\newline$ From the first group $5s^3 + 10s^2$ , we can factor out $5s^2$ , which gives us $5s^2(s + 2)$ . $\newline$ From the second group $-s - 2$ , we can factor out $-1$ , which gives us $-1(s + 2)$ .
Write Factored Expression: Write the expression with the factored groups. $\newline$ Now we have $5s^2(s + 2) - 1(s + 2)$ .
Factor Common Binomial: Factor out the common binomial factor. $\newline$ We can see that $(s + 2)$ is a common factor in both terms, so we factor it out to get $(s + 2)(5s^2 - 1)$ .
Factor Difference of Squares: Factor the difference of squares if possible. $\newline$ The term $5s^2 - 1$ is a difference of squares, as it can be written as $(\sqrt{5s})^2 - 1^2$ . We can factor this as $(5s^2 - 1) = (\sqrt{5s} + 1)(\sqrt{5s} - 1)$ .
Write Final Form: Write the final factored form. $\newline$ The fully factored form of the polynomial is $(s + 2)(\sqrt{5}s + 1)(\sqrt{5}s - 1)$ .