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GCD of Polynomials

State whether...

Question

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

$x^{2} - 25, x^{2} - 2 x - 35$ and $x^{2} - 12 x + 35$ is $1; (x - 5) (x + 5) (x - 7)$
If true then enter $1$ and if false then enter $0$

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Solution

Factorizing $x^{2} - 25, x^{2} - 2 x - 35$ and $x^{2} - 12 x + 35,$
$x^{2} - 2 = (x - 5) (x + 5)$
$x^{2} - 2 x - 35 = (x + 5) (x - 7)$
$x^{2} - 12 x + 35 = (x - 7) (x - 5)$
H.C.F. $= 1$
L.C.M. $= (x - 5) (x + 5) (x - 7)$

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