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Factor.\newline3r3r2+9r33r^3 - r^2 + 9r - 3

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Q. Factor.\newline3r3r2+9r33r^3 - r^2 + 9r - 3
  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 common factor in all terms is 11, which does not simplify the expression further.\newlineStep Output: No common factor 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 together and the last two terms together: 3r3r23r^3 - r^2 + 9r39r - 3.\newlineStep Output: Grouped terms: 3r3r23r^3 - r^2 + 9r39r - 3.
  3. Factor Each Group: Step Title: Factor Each Group\newlineConcise Step Description: Factor out the greatest common factor from each group.\newlineStep Calculation: From the first group, factor out r2r^2, and from the second group, factor out 33.\newlineStep Output: Factored groups: r2(3r1)+3(3r1)r^2(3r - 1) + 3(3r - 1).
  4. Factor Out the 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 (3r1)(3r - 1).\newlineStep Output: Factored expression: (3r1)(r2+3)(3r - 1)(r^2 + 3).