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Write the Factored Form of the given expression: 2s^(2)-3s-2=0

Write the Factored Form of the given expression: 2s2−3s−2=02s^{2}-3s-2=0

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Full solution

Q. Write the Factored Form of the given expression: 2s2−3s−2=02s^{2}-3s-2=0
  1. Identify Coefficients: Step Title: Identify the Coefficients\newlineReasoning: Identify the coefficients of the quadratic equation, which are 22, −3-3, and −2-2.\newlineCalculation: Coefficients are 22, −3-3, −2-2.\newlineMath Error Check:
  2. Find Factors: Step Title: Find the Factors\newlineReasoning: Find two numbers that multiply to −4-4 (product of the first and last coefficients, 2∗(−2)2*(-2)) and add to −3-3 (the middle coefficient).\newlineCalculation: Factors of −4-4 that add up to −3-3 are −4-4 and 11.\newlineMath Error Check:
  3. Write Factored Form: Step Title: Write the Factored Form\newlineReasoning: Use the factors to split the middle term and factor by grouping.\newlineCalculation: 2s2−4s+s−2=(2s2−4s)+(s−2)=2s(s−2)+1(s−2)=(2s+1)(s−2)2s^2 - 4s + s - 2 = (2s^2 - 4s) + (s - 2) = 2s(s - 2) + 1(s - 2) = (2s + 1)(s - 2).\newlineMath Error Check:

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