Q. 3 E3.8( 8 Votes )

# Let’s find G.C.D of the following algebraic expression:

a^{2}-1, a^{3}-1, a^{2} + a-2

Answer :

Factors of a^{2}-1=(a + 1)(a-1)

Factors of a^{3}-1=(a-1)(a^{2} + a + 1) … (from properties)

Factors of a^{2} + a-2

=(a^{2} + a-2)

=(a^{2} + 2a-a-2)

=[{a(a + 2)-1(a + 2)}]

=[{(a + 2)(a-1)}]

=(a + 2)×(a-1)

GCD is the greatest common divisor, which is equal to the product of all the common divisors.

∴the GCD of a^{2}-1, a^{3}-1, a^{2} + a-2 is (a-1)

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