Identify Common Factors: Step Title: Identify Common FactorsConcise Step Description: Look for any common factors in all terms of the polynomial.Step Calculation: The common factor in all terms is 1, which does not simplify the expression further.Step Output: No common factor other than 1.
Group Terms: Step Title: Group TermsConcise Step Description: Group terms to factor by grouping.Step Calculation: Group the first two terms together and the last two terms together: 3r3−r2 + 9r−3.Step Output: Grouped terms: 3r3−r2 + 9r−3.
Factor Each Group: Step Title: Factor Each GroupConcise Step Description: Factor out the greatest common factor from each group.Step Calculation: From the first group, factor out r2, and from the second group, factor out 3.Step Output: Factored groups: r2(3r−1)+3(3r−1).
Factor Out the 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 (3r−1).Step Output: Factored expression: (3r−1)(r2+3).