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GCD of Polynomials

State whether...

Question

State whether True or False.
The H.C.F. and L.C.M. of:

$a^{2} + a - 6, a^{2} + 2 a - 8$ and $2 a^{2} - 5 a + 2$ is $(a - 2); (a + 3) (a + 4) (a - 2) (2 a - 1)$
If true then enter $1$ and if false then enter $0$

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Solution

Factorizing $a^{2} + a - 6, a^{2} + 2 a - 8$ and $2 a^{2} - 5 a + 2,$
$a^{2} + a - 6 = (a + 3) (a - 2)$
$a^{2} + 2 a - 8 = (a + 4) (a - 2)$
$2 a^{2} - 5 a + 2 = (a - 2) (2 a - 1)$
H.C.F. $= (a - 2)$
L.C.M. $= (a + 3) (a + 4) (a - 2) (2 a - 1)$

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