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Factor.\newline16u38u2+10u516u^3 - 8u^2 + 10u - 5

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Q. Factor.\newline16u38u2+10u516u^3 - 8u^2 + 10u - 5
  1. Identify Common Factors: Step Title: Identify Common Factors\newlineConcise Step Description: Look for any common factors in all terms of the polynomial.\newlineStep Calculation: The greatest common factor of 16u316u^3, 8u28u^2, 10u10u, and 55 is 11.\newlineStep Output: No common factors other than 11.
  2. Group Terms: Step Title: Group Terms\newlineConcise Step Description: Group terms to factor by grouping.\newlineStep Calculation: Group the first two terms and the last two terms: 16u38u216u^3 - 8u^2 + 10u510u - 5.\newlineStep Output: Grouped terms: 16u38u216u^3 - 8u^2 + 10u510u - 5.
  3. Factor Out GCF from Each Group: Step Title: Factor Out the Greatest Common Factor from Each Group\newlineConcise Step Description: Factor out the greatest common factor from each group.\newlineStep Calculation: Factor out 8u28u^2 from the first group and 55 from the second group: 8u2(2u1)+5(2u1)8u^2(2u - 1) + 5(2u - 1).\newlineStep Output: Factored groups: 8u2(2u1)+5(2u1)8u^2(2u - 1) + 5(2u - 1).
  4. Factor Out Common Binomial Factor: Step Title: Factor Out the Common Binomial Factor\newlineConcise Step Description: Factor out the common binomial factor from the factored groups.\newlineStep Calculation: The common binomial factor is (2u1)(2u - 1). Factor this out: (2u1)(8u2+5)(2u - 1)(8u^2 + 5).\newlineStep Output: Factored form: (2u1)(8u2+5)(2u - 1)(8u^2 + 5).