Q. 5 A
Let’s find the G.C.D and L.C.M. of the following expressions:
x3-8, x2 + 3x-10, x3 + 2x2-8x
Answer :
Factors of x3-8
=(x-2)(x2 + 2x + 4)
Factors of x2 + 3x-10
= x2 + 5x-2x-10
=x(x + 5)-2(x + 5)
=(x + 5)(x-2)
Factors of x3 + 2x2-8x
=x(x2 + 2x-8)
=x(x2 + 4x-2x-8)
=x{x(x + 4)-2(x + 4)}
=x(x + 4)(x-2)
LCM is the lowest common multiple, which is the product of all the common factors taken once and the remaining factors as it is.
∴ the LCM of x3-8, x2 + 3x-10, x3 + 2x2-8x is x(x-2)(x2 + 2x + 4) (x + 4)(x + 5)
GCD is the greatest common divisor, which is equal to the product of all the common divisors.
∴ the GCD is (x-2)
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