Factor completely. x^(3)-8x^(2)-2x+16=

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Factor completely.  x^(3)-8x^(2)-2x+16=

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Identify Terms: Step Title: Identify the Terms Concise Step Description: Identify the terms of the polynomial to understand its structure. Step Calculation: The polynomial is x^3 - 8x^2 - 2x + 16, which has four terms. Step Output: Terms: x^3, -8x^2, -2x, +16Group Terms: Step Title: Group the Terms Concise Step Description: Group the terms in pairs to facilitate factoring by grouping. Step Calculation: Group the terms as (x^3 - 8x^2) and (-2x + 16). Step Output: Grouped Terms: (x^3 - 8x^2), (-2x + 16)Factor by Grouping: Step Title: Factor by Grouping Concise Step Description: Factor out the greatest common factor from each group. Step Calculation: From (x^3 - 8x^2), factor out x^2 to get x^2(x - 8). From (-2x + 16), factor out -2 to get -2(x - 8). Step Output: Factored Groups: x^2(x - 8), -2(x - 8)Factor Out Common Binomial: Step Title: Factor Out the Common Binomial Concise Step Description: Factor out the common binomial factor from the factored groups. Step Calculation: The common binomial factor is (x - 8). Factoring it out, we get (x - 8)(x^2 - 2). Step Output: Factored Form: (x - 8)(x^2 - 2)Check for Further Factoring: Step Title: Check for Further Factoring Concise Step Description: Check if the remaining quadratic can be factored further. Step Calculation: The quadratic x^2 - 2 is a difference of squares and can be factored as (x + √2)(x - √2). Step Output: Further Factored Form: (x - 8)(x + √2)(x - √2)

Factor completely. $\newline$ $x^{3}-8 x^{2}-2 x+16=$

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Factor completely.\newlinex3−8x2−2x+16= x^{3}-8 x^{2}-2 x+16= x3−8x2−2x+16=

Factor completely. $\newline$ $x^{3}-8 x^{2}-2 x+16=$