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Factor.\newline9m36m215m+109m^3 - 6m^2 - 15m + 10

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Q. Factor.\newline9m36m215m+109m^3 - 6m^2 - 15m + 10
  1. Identify Common Factors: Look for common factors in pairs of terms.\newlineWe can try to factor by grouping, which involves combining terms that have common factors. We'll look at the first two terms and the last two terms separately.
  2. Factor First Two Terms: Factor out the greatest common factor from the first two terms.\newlineThe first two terms are 9m39m^3 and 6m2-6m^2. The greatest common factor is 3m23m^2.\newline9m36m2=3m2(3m2)9m^3 - 6m^2 = 3m^2(3m - 2)
  3. Factor Last Two Terms: Factor out the greatest common factor from the last two terms.\newlineThe last two terms are 15m-15m and +10+10. The greatest common factor is 55.\newline15m+10=5(3m2)-15m + 10 = -5(3m - 2)
  4. Combine Factors: Write the expression with the factors found.\newlineWe now have:\newline3m2(3m2)5(3m2)3m^2(3m - 2) - 5(3m - 2)\newlineNotice that (3m2)(3m - 2) is a common factor.
  5. Factor Out Common Factor: Factor out the common factor of (3m2)(3m - 2).\newlineWe can factor (3m2)(3m - 2) out of both terms.\newline3m2(3m2)5(3m2)=(3m2)(3m25)3m^2(3m - 2) - 5(3m - 2) = (3m - 2)(3m^2 - 5)