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Name 
qquad Algebra 2 
qquad Score 
qquad Date 
qquad Algebra 2 Section 9 - 5 Quiz
Find the least common multiple of each pair of polynomials. Show your work! 
(2pts)


12x^(2)y^(2) and 
18 xy^(3)

12x^(2)y^(2)=2^(2)×3×x^(2)×y^(2)

3x^(2)-27 and 
x^(2)+6x+9

Name \qquad Algebra 22 \qquad Score \qquad Date \qquad Algebra 22 Section 99 - 55 Quiz\newlineFind the least common multiple of each pair of polynomials. Show your work! (2pts) (2 \mathrm{pts}) \newline11) 12x2y2 12 x^{2} y^{2} and 18xy3 18 x y^{3} \newline12x2y2=22×3×x2×y2 12 x^{2} y^{2}=2^{2} \times 3 \times x^{2} \times y^{2} \newline22) 3x227 3 x^{2}-27 and x2+6x+9 x^{2}+6 x+9

Full solution

Q. Name \qquad Algebra 22 \qquad Score \qquad Date \qquad Algebra 22 Section 99 - 55 Quiz\newlineFind the least common multiple of each pair of polynomials. Show your work! (2pts) (2 \mathrm{pts}) \newline11) 12x2y2 12 x^{2} y^{2} and 18xy3 18 x y^{3} \newline12x2y2=22×3×x2×y2 12 x^{2} y^{2}=2^{2} \times 3 \times x^{2} \times y^{2} \newline22) 3x227 3 x^{2}-27 and x2+6x+9 x^{2}+6 x+9
  1. Find LCM of 12x2y212x^2y^2 and 18xy318xy^3: First, let's find the LCM of 12x2y212x^2y^2 and 18xy318xy^3. Factor each polynomial to its prime factors: 12x2y2=22×3×x2×y212x^2y^2 = 2^2 \times 3 \times x^2 \times y^2 18xy3=2×32×x×y318xy^3 = 2 \times 3^2 \times x \times y^3 Now, take the highest powers of each prime factor to get the LCM: LCM=22×32×x2×y3LCM = 2^2 \times 3^2 \times x^2 \times y^3
  2. Factorize polynomials: Next, find the LCM of 3x2273x^2 - 27 and x2+6x+9x^2 + 6x + 9. First, factor each polynomial: 3x227=3(x29)=3(x+3)(x3)3x^2 - 27 = 3(x^2 - 9) = 3(x + 3)(x - 3) x2+6x+9=(x+3)(x+3)x^2 + 6x + 9 = (x + 3)(x + 3) The LCM is the product of the distinct factors raised to their highest powers: LCM=3(x+3)(x3)(x+3)LCM = 3(x + 3)(x - 3)(x + 3)

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