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Factor.\newline12m3+18m2+10m+1512m^3 + 18m^2 + 10m + 15

Full solution

Q. Factor.\newline12m3+18m2+10m+1512m^3 + 18m^2 + 10m + 15
  1. Identify Common Factors: Look for common factors in each pair of terms.\newlineFirst, we look at the terms 12m312m^3 and 18m218m^2 and find the greatest common factor (GCF) which is 6m26m^2.\newline12m3+18m2=6m2(2m+3)12m^3 + 18m^2 = 6m^2(2m + 3)
  2. Find GCF for 12m312m^3 and 18m218m^2: Now, we look at the terms 10m10m and 1515 and find their GCF which is 55.$10m+15=5(2m+3)\$10m + 15 = 5(2m + 3))
  3. Find GCF for 10m10m and 1515: We have factored both pairs of terms:\newline12m3+18m2=6m2(2m+3)12m^3 + 18m^2 = 6m^2(2m + 3)\newline10m+15=5(2m+3)10m + 15 = 5(2m + 3)\newlineNow, we can see that both factored expressions contain the common binomial factor (2m+3)(2m + 3).
  4. Factor Pairs of Terms: Factor out the common binomial factor (2m+3)(2m + 3) from both expressions.\newlineFactored form: (6m2+5)(2m+3)(6m^2 + 5)(2m + 3)