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Factor.\newline14w36w2+7w314w^3 - 6w^2 + 7w - 3

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Q. Factor.\newline14w36w2+7w314w^3 - 6w^2 + 7w - 3
  1. Identify Common Factors: Look for common factors in each pair of terms. We can pair the terms as (14w36w2)(14w^3 - 6w^2) and (7w3)(7w - 3) to look for common factors.
  2. Factor First Pair: Factor out the greatest common factor from the first pair of terms.\newlineThe greatest common factor of 14w314w^3 and 6w26w^2 is 2w22w^2.\newlineSo, 14w36w2=2w2(7w3)14w^3 - 6w^2 = 2w^2(7w - 3).
  3. Factor Second Pair: Factor out the greatest common factor from the second pair of terms.\newlineThe greatest common factor of 7w7w and 33 is 11, and there is no common factor other than 11.\newlineSo, 7w37w - 3 remains unchanged.
  4. Check for Common Binomial Factor: Check if there is a common binomial factor in both expressions.\newlineWe have 2w2(7w3)2w^2(7w - 3) and 7w37w - 3. The common binomial factor is (7w3)(7w - 3).
  5. Factor out Common Binomial Factor: Factor out the common binomial factor.\newlineWe can write the expression as (7w3)(2w2+1)(7w - 3)(2w^2 + 1).