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Factor.\newline7q37q2+9q97q^3 - 7q^2 + 9q - 9

Full solution

Q. Factor.\newline7q37q2+9q97q^3 - 7q^2 + 9q - 9
  1. Group Terms: Look for common factors in pairs of terms.\newlineWe will first group the terms into pairs and look for common factors in each pair.\newlineGroup the terms: (7q37q2)+(9q9)(7q^3 - 7q^2) + (9q - 9).
  2. Factor First Pair: Factor out the common factor from the first pair of terms.\newlineFactor out 7q27q^2 from the first group: 7q2(q1)7q^2(q - 1).
  3. Factor Second Pair: Factor out the common factor from the second pair of terms.\newlineFactor out 99 from the second group: 9(q1)9(q - 1).
  4. Write Findings: Write down what we have found so far.\newlineWe have: 7q2(q1)+9(q1)7q^2(q - 1) + 9(q - 1).\newlineNotice that (q1)(q - 1) is a common factor in both terms.
  5. Factor Common Factor: Factor out the common factor (q1)(q - 1).\newlineFactor (q1)(q - 1) out of both terms: (q1)(7q2+9)(q - 1)(7q^2 + 9).
  6. Check Further Factoring: Check for any further factoring possibilities.\newlineThe second term 7q2+97q^2 + 9 does not have any common factors and cannot be factored further.