Factor. 6x^3 + 12x^2 - x - 2 ______

Group Terms: Group the terms to find common factors. We can group the terms as follows: (6x^3 + 12x^2) and (-x - 2).Factor Common Factors: Factor out the greatest common factor from each group. From the first group (6x^3 + 12x^2), we can factor out 6x^2, which gives us 6x^2(x + 2). From the second group (-x - 2), we can factor out -1, which gives us -1(x + 2).Write Factored Expression: Write the expression with the factored groups. Now we have 6x^2(x + 2) - 1(x + 2).Factor Common Binomial: Factor out the common binomial factor. We can see that (x + 2) is a common factor in both terms, so we factor it out to get (x + 2)(6x^2 - 1).Check Quadratic Factorization: Check if the remaining quadratic can be factored further. The quadratic 6x^2 - 1 is a difference of squares, which can be factored as (sqrt(6)x - 1)(sqrt(6)x + 1).Write Final Form: Write the final factored form. The final factored form of the polynomial is (x + 2)(sqrt(6)x - 1)(sqrt(6)x + 1).

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6x^3 + 12x^2 - x - 2

Group Terms: Group the terms to find common factors. $\newline$ We can group the terms as follows: $(6x^3 + 12x^2)$ and $(-x - 2)$ .
Factor Common Factors: Factor out the greatest common factor from each group. $\newline$ From the first group $6x^3 + 12x^2$ , we can factor out $6x^2$ , which gives us $6x^2(x + 2)$ . $\newline$ From the second group $-x - 2$ , we can factor out $-1$ , which gives us $-1(x + 2)$ .
Write Factored Expression: Write the expression with the factored groups. $\newline$ Now we have $6x^2(x + 2) - 1(x + 2)$ .
Factor Common Binomial: Factor out the common binomial factor. $\newline$ We can see that $(x + 2)$ is a common factor in both terms, so we factor it out to get $(x + 2)(6x^2 - 1)$ .
Check Quadratic Factorization: Check if the remaining quadratic can be factored further. The quadratic $6x^2 - 1$ is a difference of squares, which can be factored as $(\sqrt{6}x - 1)(\sqrt{6}x + 1)$ .
Write Final Form: Write the final factored form. $\newline$ The final factored form of the polynomial is $(x + 2)(\sqrt{6}x - 1)(\sqrt{6}x + 1)$ .