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Factor.\newline6m36m2+m16m^3 - 6m^2 + m - 1

Full solution

Q. Factor.\newline6m36m2+m16m^3 - 6m^2 + m - 1
  1. Grouping for factoring: Group terms to prepare for factoring by grouping. Group the first two terms and the last two terms separately. 6m36m26m^3 - 6m^2 + m1m - 1
  2. Factor out common factors: Factor out the greatest common factor from each group.\newlineFrom the first group, factor out 6m26m^2. From the second group, factor out 11.\newline6m2(m1)+1(m1)6m^2(m - 1) + 1(m - 1)
  3. Factor out (m1)(m - 1): Notice that (m1)(m - 1) is a common factor in both groups.\newlineFactor out (m1)(m - 1) from the entire expression.\newline(m1)(6m2+1)(m - 1)(6m^2 + 1)
  4. Check for further factoring: Check to see if the factored terms can be factored further. \newline6m2+16m^2 + 1 is a sum of squares and cannot be factored over the real numbers. \newlineThe factored form is (m1)(6m2+1)(m - 1)(6m^2 + 1).