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Factor.\newline10n3+10n2−3n−310n^3 + 10n^2 - 3n - 3

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Full solution

Q. Factor.\newline10n3+10n2−3n−310n^3 + 10n^2 - 3n - 3
  1. Group Terms for Factoring: Group terms that can be factored by grouping.\newlineGroup the first two terms and the last two terms separately.\newline10n3+10n2−3n−310n^3 + 10n^2 - 3n - 3 can be grouped as (10n3+10n2)+(−3n−3)(10n^3 + 10n^2) + (-3n - 3).
  2. Factor Out Common Factors: Factor out the greatest common factor from each group.\newlineFrom the first group 10n3+10n210n^3 + 10n^2, factor out 10n210n^2.\newline10n3+10n2=10n2(n+1)10n^3 + 10n^2 = 10n^2(n + 1).\newlineFrom the second group −3n−3-3n - 3, factor out −3-3.\newline−3n−3=−3(n+1)-3n - 3 = -3(n + 1).
  3. Write Factored Expression: Write the expression with the factored groups.\newlineThe expression now looks like this: 10n2(n+1)−3(n+1)10n^2(n + 1) - 3(n + 1).
  4. Factor Out Common Binomial: Factor out the common binomial factor.\newlineBoth terms have a common factor of (n+1)(n + 1).\newlineFactor out (n+1)(n + 1) from both terms.\newlineThe factored form is (n+1)(10n2−3)(n + 1)(10n^2 - 3).

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