Find the LCM of (x + 3) $(6 x^{2} + 5 x + 4) a n d (2 x^{2} + 7 x + 3)$ (x + 3)

(2 x + 1) (x + 3) (3 x + 4)

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(4 x^{2} + 1) (x + 3)^{2} (3 x + 4)

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2 (x + 3)^{2} (6 x^{2} + 5 x + 4) (x + \frac{1}{2})

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(2x - 1)(x + 3)(3x + 4)

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Solution

The correct option is C $2 (x + 3)^{2} (6 x^{2} + 5 x + 4) (x + \frac{1}{2})$
For the LCM of polynomials write down the highest powers of all available factors of all the polynomials. The correct answer would be $2 (x + 3)^{2} (6 x^{2} + 5 x + 4) (x + \frac{1}{2})$ .

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∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{2} - 1 & x^{2} + 2 x + 1 & 2 x^{2} + 3 x + 1 2 x^{2} + x - 1 & 2 x^{2} + 5 x - 3 & 4 x^{2} + 4 x - 3 6 x^{2} - x - 2 & 6 x^{2} - 7 x + 2 & 12 x^{2} - 5 x - 2 \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

D E ∥ B C

A D = 3 x - 2

A E = 5 x - 4

B D = 7 X - 4

B D - 7 x - 5

C E = 5 x - 3

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