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Find the least common multiple of each pair of polynomials. Show your work! ( 2 pts) 2) 3x^(2)-27 and x^(2)+6x+9

Find the least common multiple of each pair of polynomials. Show your work! ( 22 pts)\newline22) 3x2−27 3 x^{2}-27 and x2+6x+9 x^{2}+6 x+9

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Q. Find the least common multiple of each pair of polynomials. Show your work! ( 22 pts)\newline22) 3x2−27 3 x^{2}-27 and x2+6x+9 x^{2}+6 x+9
  1. Factor Polynomials: Factor both polynomials to find their prime factors.\newline3x2−273x^2 - 27 can be factored as 3(x2−9)3(x^2 - 9), which further factors as 3(x+3)(x−3)3(x + 3)(x - 3).\newlinex2+6x+9x^2 + 6x + 9 can be factored as (x+3)(x+3)(x + 3)(x + 3) or (x+3)2(x + 3)^2.
  2. Identify LCM: Identify the least common multiple of the polynomials.\newlineThe LCM of the polynomials will be the product of the highest powers of all the factors found in the polynomials.\newlineSo, the LCM is 3(x+3)2(x−3)3(x + 3)^2(x - 3).

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