Find the GCD of the following pairs of polynomials using division algorithm.

2x³ + 2x² + 2x + 2, 6x³ + 12x² + 6x + 12

2x³ + 2x² + 2x + 2 then put x = – 1

Since, – 2 + 2 – 2 + 2 = 0

Then the equation is divisible by x + 1, using division algorithm method.

(x + 1)(2x² + 2) = 2(x + 1)(x² + 1)

In equation second,

6x³ + 12x² + 6x + 12,put x = – 2

Then, – 48 + 48 – 12 + 12 = 0

Then the equation is divisible by x + 2, using division algorithm method.

(x + 2)(6x² + 6) = 2 × 3(x + 2)(x² + 1)

Greatest common divisor = 2(x² + 1)