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

Question

Bytelearn · Accepted Answer

Identify GCF: Step Title: Identify the Greatest Common Factor (GCF) Concise Step Description: Determine if there is a greatest common factor that can be factored out from all terms of the polynomial. Step Calculation: The GCF of 16k^3, 8k^2, 2k, and 1 is 1. Step Output: GCF: 1Check Quadratic Form: Step Title: Check for a Quadratic Form Concise Step Description: Check if the polynomial can be written in a quadratic form by grouping. Step Calculation: The polynomial does not have a clear quadratic form, but we can try to group terms to see if a pattern emerges. Step Output: No clear quadratic form.Group Terms: Step Title: Group Terms Concise Step Description: Group terms to see if a pattern emerges that can be factored. Step Calculation: Group the terms as (16k^3 + 8k^2) + (2k + 1). Step Output: Grouped terms: (16k^3 + 8k^2) and (2k + 1).Factor by Grouping: Step Title: Factor by Grouping Concise Step Description: Factor out the common factors in each group. Step Calculation: In the first group, factor out 8k^2, resulting in 8k^2(2k + 1). The second group is already in the form (2k + 1). Step Output: Factored groups: 8k^2(2k + 1) and (2k + 1).Factor Out Binomial: Step Title: Factor Out the Common Binomial Concise Step Description: Factor out the common binomial from the factored groups. Step Calculation: The common binomial is (2k + 1), so factor it out from both groups. Step Output: Factored polynomial: (2k + 1)(8k^2 + 1).

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

Full solution

More problems from Factor polynomials

Related topics

Factor.\newline16k3+8k2+2k+116k^3 + 8k^2 + 2k + 116k3+8k2+2k+1

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