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)