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Factor.\newlinen2+5n+6n^2 + 5n + 6

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Q. Factor.\newlinen2+5n+6n^2 + 5n + 6
  1. Identify Coefficients: Identify the coefficients for n2n^2, nn, and the constant term.\newlineThe quadratic expression is n2+5n+6n^2 + 5n + 6. Here, the coefficient of n2n^2 (aa) is 11, the coefficient of nn (bb) is 55, and the constant term (cc) is nn00.
  2. Find Multiplying Numbers: Determine two numbers that multiply to give the constant term cc and add up to the coefficient of nn (bb).\newlineWe need to find two numbers that multiply to 66 and add up to 55. The numbers 22 and 33 satisfy these conditions because 2×3=62 \times 3 = 6 and 2+3=52 + 3 = 5.
  3. Write Factored Form: Write the factored form using the two numbers found in the previous step.\newlineThe factored form of the quadratic expression n2+5n+6n^2 + 5n + 6 is (n+2)(n+3)(n + 2)(n + 3).