Find the LCM of $m^{2} - 9 m - 22, m^{2} - 8 m - 33, m^{2} + 5 m + 6$

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Solution

We know that $L C M$ is the least common multiple.

Factorise $m^{2} - 9 m - 22$ as follows:

$m^{2} - 9 m - 22 = m^{2} - 11 m + 2 m - 22 = m (m - 11) + 2 (m - 11) = (m + 2) (m - 11)$

Now, factorise $m^{2} - 8 m - 33$ as follows:

$m^{2} - 8 m - 33 = m^{2} - 11 m + 3 m - 33 = m (m - 11) + 3 (m - 11) = (m + 3) (m - 11)$

Finally, factorise $m^{2} + 5 m + 6$ as follows:

$m^{2} + 5 m + 6 = m^{2} + 3 m + 2 m + 6 = m (m + 3) + 2 (m + 3) = (m + 3) (m + 2)$

Therefore, the least common multiple between the polynomials $m^{2} - 9 m - 22$ , $m^{2} - 8 m - 33$ and $m^{2} + 5 m + 6$ is:

$L C M = (m + 2) (m + 3) (m - 11)$

Hence, the $L C M$ is $(m + 2) (m + 3) (m - 11)$ .

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Find the third side of a triangle whose two sides are $(3 m^{2} - 5 m$ ) and $(4 m^{2} + 12$ ) and perimeter is $(8 m^{2} - 9 m + 4$ ).

Find the third side of a triangle whose perimeter is $8 m^{2} - 9 m + 4$ and two of its sides are $3 m^{2} - 5 m$ and $4 m^{2} + 12$ .

The GCD of m²-3m-18 and m²+5m+6 is:

m^{2} + 5 m + 6

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