Q. 3 D3.6( 13 Votes )
Let’s find G.C.D of the following algebraic expression:
x2-1, x2-2x + 1, x3 + x2-2x
Answer :
Factors of x2-1=(x + 1)(x-1)
Factors of x2-2x + 1
x2-2x + 1=x2-x-x + 1
=x(x-1)-1(x-1)
=(x-1)2
=(x-1)×(x-1)
Factors of x3 + x2-2x
x3 + x2-2x=x(x2 + x-2)
=x(x2 + 2x-x-2)
=x[{x(x + 2)-1(x + 2)}]
=x[{(x + 2)(x-1)}]
=x×(x + 2)×(x-1)
GCD is the greatest common divisor, which is equal to the product of all the common divisors.
∴ the GCD of x2-1, x2-2x + 1, x3 + x2-2x is (x-1)
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