Find the gcd of x^2-x-2 and x^3-7z+6 and express as a linear combination of them
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x^2 - x - 2
= x^2 - 2x + x - 2
= x ( x - 2 ) + 1 ( x - 2 )
= ( x - 2 )( x + 1 )
x^2 - 7x + 6
= x^2 - 6x - 1x + 6
= x ( x - 6 ) - 1 ( x - 6 )
= ( x - 6 )( x - 1 )
so G.C.D = x - 1
= x^2 - 2x + x - 2
= x ( x - 2 ) + 1 ( x - 2 )
= ( x - 2 )( x + 1 )
x^2 - 7x + 6
= x^2 - 6x - 1x + 6
= x ( x - 6 ) - 1 ( x - 6 )
= ( x - 6 )( x - 1 )
so G.C.D = x - 1
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