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mial: 2x^(2)+19 x+42

mial:\newline2x2+19x+42 2 x^{2}+19 x+42

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Full solution

Q. mial:\newline2x2+19x+42 2 x^{2}+19 x+42
  1. Factor Quadratic Expression: question_prompt: Factor the quadratic expression 2x2+19x+422x^2 + 19x + 42.
  2. Find Multiplying Numbers: Step 11: Look for two numbers that multiply to 2×422\times42 (which is 8484) and add up to 1919.
  3. Identify Correct Numbers: Step 22: The numbers are 1212 and 77 because 12×7=8412 \times 7 = 84 and 12+7=1912+7 = 19.
  4. Rewrite Middle Term: Step 33: Rewrite the middle term using the numbers 1212 and 77: 2x2+12x+7x+422x^2 + 12x + 7x + 42.
  5. Factor by Grouping: Step 44: Factor by grouping. Group the first two terms and the last two terms: (2x2+12x)+(7x+42)(2x^2 + 12x) + (7x + 42).
  6. Factor out Common Factor: Step 55: Factor out the common factor from each group: 2x(x+6)+7(x+6)2x(x + 6) + 7(x + 6).
  7. Final Factorization: Step 66: Factor out the common binomial (x+6)(x + 6): (2x+7)(x+6)(2x + 7)(x + 6).

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