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GCD of Polynomials

State whether...

Question

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

$a^{3} - 36 a$ and $a^{3} + 2 a^{2} - 48 a$ is $a (a - 6); a (a + 6) (a - 6) (a + 8)$
If true then enter $1$ and if false then enter $0$

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Solution

Factorizing $a^{3} - 36 a, a^{3} + 2 a^{2} - 48,$
$a^{3} - 36 a = a (a^{2} - 36) = a (a + 6) (a - 6)$
$a^{3} + 2 a^{2} - 48 = a (a^{2} + 2 a - 48) = a (a - 6) (a + 8)$
H.C.F. $= a (a - 6)$
L.C.M. $= a (a + 6) (a - 6) (a + 8)$

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