Factor. 16v^3 + 8v^2 + 2v + 1 ______

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Identify GCF: Step Title: Identify the Greatest Common Factor (GCF) Concise Step Description: Determine the greatest common factor of all the terms in the polynomial. Step Calculation: The GCF of 16v^3, 8v^2, 2v, and 1 is 1. Step Output: GCF: 1Check Variable Factor: Step Title: Check for a Common Variable Factor Concise Step Description: Check if there is a common variable factor that can be factored out from all terms. Step Calculation: All terms have at least one factor of v, so we can factor out v. Step Output: Common variable factor: vFactor Out GCF: Step Title: Factor Out the GCF Concise Step Description: Factor out the greatest common factor from each term in the polynomial. Step Calculation: Factoring out v, we get v(16v^2 + 8v + 2) + 1. Step Output: Factored polynomial with GCF: v(16v^2 + 8v + 2) + 1Recognize Pattern: Step Title: Recognize a Pattern Concise Step Description: Recognize if the remaining polynomial is a special product or can be factored further. Step Calculation: The polynomial inside the parentheses is not a perfect square, and there is no obvious factorization. The term outside the parentheses is a constant. Step Output: No further factorization is apparent.Attempt Division: Step Title: Attempt Polynomial Division or Synthetic Division Concise Step Description: Since the polynomial does not factor easily, attempt polynomial division or synthetic division to find factors. Step Calculation: Polynomial division or synthetic division may be used here, but there is no clear divisor to use. Step Output: No clear divisor for polynomial division or synthetic division.Check Binomial Factor: Step Title: Check for a Binomial Factor Concise Step Description: Check if the polynomial can be factored as a product of binomials. Step Calculation: The polynomial does not fit the pattern of a binomial product such as (ax + b)(cx + d). Step Output: No binomial factorization is possible.Conclusion: Step Title: Conclusion Concise Step Description: Conclude that the polynomial is either prime or requires a more complex factorization method. Step Calculation: Without a clear factorization pattern, the polynomial is either prime or requires a method beyond basic factorization techniques. Step Output: The polynomial may be prime or require advanced factorization.

Factor. $\newline$ $16v^3 + 8v^2 + 2v + 1$

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Factor.\newline16v3+8v2+2v+116v^3 + 8v^2 + 2v + 116v3+8v2+2v+1

Factor. $\newline$ $16v^3 + 8v^2 + 2v + 1$