Q. 3 L4.6( 8 Votes )

# Let’s find G.C.D of the following algebraic expression:x3-3x2-10x, x3 + 6x2 + 8x, x4-5x3-14x2

Factors of x3-3x2-10x

=x(x2-3x-10)

=x(x2-5x + 2x-10)

=[x{x(x-5) + 2(x-5)}]

=x(x + 2)(x-5)

Factors of x3 + 6x2 + 8x

=x(x2 + 6x + 8)

=x(x2 + 4x + 2x + 8)

=x[x(x + 4) + 2(x + 4)]

=x(x + 2)(x + 4)

Factors of x4-5x3-14x2

=x2(x2-5x-14)

= x2(x2-7x + 2x-14)

= x2{x(x-7) + 2(x-7)}

= x2 � �(x + 2)(x-7)

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

the GCD of x3-3x2-10x, x3 + 6x2 + 8x, x4-5x3-14x2 is x(x + 2)

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