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

x³-16x, 2x³ + 9x² + 4x, 2x³ + x²-28x

Factors of x³-16x

=x(x²-16)

=x(x + 4)(x-4) … (Using a²-b²=(a + b)(a-b))

Factors of 2x³ + 9x² + 4x

=x(2x² + 9x + 4)

=x(2x² + 8x + x + 4)

=x{2x(x + 4) + 1(x + 4)}

=x[{(2x + 1)(x + 4)}]

=x×(2x + 1)×(x + 4)

Factors of 2x³ + x²-28x

=x(2x² + x-28)

=x(2x² + 8x-7x-28)

=x{2x(x + 4)-7(x + 4)}

=x[{(2x-7)(x + 4)}]

=x×(2x-7)×(x + 4)

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

∴ the GCD of x³-16x, 2x³ + 9x² + 4x, 2x³ + x²-28x is x(x + 4)