find HCF of X3 - 3 x + 2 and X2 - 4 x + 3
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P (x) = x^3 - 3x + 2
= x^3 - x - 2x + 2
= x( x^2 - 1) - 2(x-1)
= x (x+1)(x-1) - 2(x-1)
= (x-1)[ x(x+1) - 2]
= (x-1)(x^2 +x - 2)
F(x) = x^2 - 4x +3
= x^2 - x - 3x + 3
= x(x-1) - 3(x-1)
= (x-1)(x-3)
HCF ( P(x), F(x) ) = (x-1)
= x^3 - x - 2x + 2
= x( x^2 - 1) - 2(x-1)
= x (x+1)(x-1) - 2(x-1)
= (x-1)[ x(x+1) - 2]
= (x-1)(x^2 +x - 2)
F(x) = x^2 - 4x +3
= x^2 - x - 3x + 3
= x(x-1) - 3(x-1)
= (x-1)(x-3)
HCF ( P(x), F(x) ) = (x-1)
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