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

x³ – 3x² + 4x – 12, x⁴ + x³ + 4x² + 4x

According to the question,

x³ – 3x² + 4x – 12,then put x = 3

then,27 – 27 + 12 – 12 = 0

Then the equation is divisible by x – 3, using division algorithm method.

(x – 3)(x² + 4) = (x – 3)(x² + 4)

In equation second,

x⁴ + x³ + 4x² + 4x,put x = – 1

then, 1 – 1 + 4 – 4 = 0,

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

(x + 1)(x³ + 4x) = x(x + 1)(x² + 4)

Greatest common divisor = (x² + 4)