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GCD of Polynomials

State whether...

Question

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

$2 a^{2} - a - 3, (2 a - 3)^{2}$ and $4 a^{2} - 9$ is $(2 a - 3); (2 a + 3) (a + 1) (2 a - 3)^{2}$
If true then enter $1$ and if false then enter $0$

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Solution

Factorizing $a^{2} - a - 3, (2 a - 3)^{2}$ and $4 a^{2} - 9,$
$a^{2} - a - 3 = a (a + 3)$
$(2 a - 3)^{2} = (2 a - 3) (2 a - 3)$
$4 a^{2} - 9 = (2 a + 3) (2 a - 3)$
H.C.F. $= (2 a - 3)$
L.C.M. $= (2 a + 3) (a + 1) (2 a - 3)^{2}$

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