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Factor.\newlinew2+9w+14w^2 + 9w + 14

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Q. Factor.\newlinew2+9w+14w^2 + 9w + 14
  1. Identify Coefficients: Identify the coefficients of the quadratic expression.\newlineThe quadratic expression is w2+9w+14w^2 + 9w + 14. Here, the coefficient of w2w^2 (aa) is 11, the coefficient of ww (bb) is 99, and the constant term (cc) is 1414.
  2. Find Multiplying Numbers: Find two numbers that multiply to cc (1414) and add up to bb (99). We need to find two numbers that multiply together to give 1414 and add together to give 99. The numbers 22 and 77 fit these requirements because 2×7=142 \times 7 = 14 and 2+7=92 + 7 = 9.
  3. Write Factored Form: Write the factored form using the two numbers found.\newlineThe factored form of the quadratic expression is (w+2)(w+7)(w + 2)(w + 7), because when we expand this, we get w2+7w+2w+14w^2 + 7w + 2w + 14, which simplifies to w2+9w+14w^2 + 9w + 14.