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Factor.\newline6t312t2+7t146t^3 - 12t^2 + 7t - 14

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Q. Factor.\newline6t312t2+7t146t^3 - 12t^2 + 7t - 14
  1. Identify Common Factors: Look for common factors in each pair of terms.\newlineWe can factor by grouping. First, we look at the first two terms 6t36t^3 and 12t2-12t^2 and factor out the greatest common factor, which is 6t26t^2.\newline6t312t2=6t2(t2)6t^3 - 12t^2 = 6t^2(t - 2)
  2. Factor by Grouping: Look for common factors in the last pair of terms.\newlineNow, we look at the last two terms 7t7t and 14-14 and factor out the greatest common factor, which is 77.\newline7t14=7(t2)7t - 14 = 7(t - 2)
  3. Factor Last Pair: Write the expression with the factored groups.\newlineWe now have:\newline6t312t2+7t14=6t2(t2)+7(t2)6t^3 - 12t^2 + 7t - 14 = 6t^2(t - 2) + 7(t - 2)
  4. Write Factored Expression: Factor out the common binomial factor.\newlineWe can see that (t2)(t - 2) is a common factor in both terms.\newline6t312t2+7t14=(6t2+7)(t2)6t^3 - 12t^2 + 7t - 14 = (6t^2 + 7)(t - 2)