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Factor.\newline4s2+12s+94s^2 + 12s + 9

Full solution

Q. Factor.\newline4s2+12s+94s^2 + 12s + 9
  1. Identify Structure: Identify the structure of the quadratic expression; it's in the form as2+bs+ca s^2 + b s + c.
  2. Find Multiplying Numbers: Look for two numbers that multiply to acac (4×9=364 \times 9 = 36) and add to bb (1212).
  3. Verify Numbers: The numbers 66 and 66 work because 6×6=366 \times 6 = 36 and 6+6=126 + 6 = 12.
  4. Rewrite Middle Term: Rewrite the middle term using the numbers 66 and 66: 4s2+6s+6s+94s^2 + 6s + 6s + 9.
  5. Factor by Grouping: Factor by grouping: (4s2+6s)+(6s+9)(4s^2 + 6s) + (6s + 9).
  6. Factor Common Factor: Factor out the common factor in each group: 2s(2s+3)+3(2s+3)2s(2s + 3) + 3(2s + 3).
  7. Factor Common Binomial: Factor out the common binomial: \(2s + 33)(22s + 33)\.
  8. Final Factored Form: Write the final factored form as a square of a binomial: (2s+3)2(2s + 3)^2.