Identify Common Factors: Step Title: Identify Common FactorsConcise Step Description: Look for any common factors in all terms of the polynomial.Step Calculation: The greatest common factor of 16u3, 8u2, 10u, and 5 is 1.Step Output: No common factors other than 1.
Group Terms: Step Title: Group TermsConcise Step Description: Group terms to factor by grouping.Step Calculation: Group the first two terms and the last two terms: 16u3−8u2 + 10u−5.Step Output: Grouped terms: 16u3−8u2 + 10u−5.
Factor Out GCF from Each Group: Step Title: Factor Out the Greatest Common Factor from Each GroupConcise Step Description: Factor out the greatest common factor from each group.Step Calculation: Factor out 8u2 from the first group and 5 from the second group: 8u2(2u−1)+5(2u−1).Step Output: Factored groups: 8u2(2u−1)+5(2u−1).
Factor Out Common Binomial Factor: Step Title: Factor Out the Common Binomial FactorConcise Step Description: Factor out the common binomial factor from the factored groups.Step Calculation: The common binomial factor is (2u−1). Factor this out: (2u−1)(8u2+5).Step Output: Factored form: (2u−1)(8u2+5).