Question

Lcm of 6 (x^2+x-6),2 (x^2+3x+2),3 (x^2+5x+6)

Answer 1

Step-by-step explanation:

$\huge\underline\mathfrak\blue{Explanation}$

$6(x {}^{2} + x - 6) \\ = 2 \times 3(x {}^{2} + 3x - 2x - 6) \\ = 2 \times 3 \times x(x + 3) - 2(x + 3) \\ = 2 \times 3 \times (x - 2)(x + 3)$

$2(x {}^{2} + 3x + 2) \\ =2( x {}^{2} + 2x + x + 2) \\ = 2 \times x(x + 2) + 1(x + 2) \\ = 2(x + 1)(x + 2)$

$3(x {}^{2} + 5x + 6) \\ = 3(x {}^{2} + 3x + 2x + 6) \\ = 3 \times x(x + 3) + 2(x + 3) \\ = 3(x + 2)(x + 3)$

So, L.C.M is:-

$3 \times 2 \times (x + 1)(x + 2)(x - 2)(x + 3) \\ = 6(x + 1)(x {}^{2} - 4)(x + 3)$

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