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How to factor 4(k12+5k−24)4(k^{12}+5k-24)?

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Full solution

Q. How to factor 4(k12+5k−24)4(k^{12}+5k-24)?
  1. Identify Coefficients: Step Title: Identify the coefficients of the quadratic part\newlineReasoning: Look at the quadratic part inside the parentheses to identify the coefficients.\newlineCalculation: Coefficients are 11, 55, −24-24 for k12k^{12}, kk, and the constant term respectively.
  2. Find Constant Term Factors: Step Title: Find the factors of the constant term\newlineReasoning: Need to find two numbers that multiply to −24-24 (the constant term) and add to 55 (the coefficient of the middle term).\newlineCalculation: Factors of −24-24 that add up to 55 are 88 and −3-3.
  3. Write Factored Form: Step Title: Write the factored form of the quadratic part\newlineReasoning: Use the factors found to write the quadratic part in its factored form.\newlineCalculation: The factored form inside the parentheses is (k+8)(k−3)(k + 8)(k - 3).

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