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

3x³ + 18x² + 33x + 18, 3x² + 13x + 10

According to the question,

3x³ + 18x² + 33x + 18 then put x = – 1 in that equation

put x = – 1

then, – 3 + 18 – 33 + 18 = 0

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

(x + 1)(3x² + 15x + 18) = (x + 1)[3x² + 9x + 6x + 18]

= (x + 1)[3x(x + 3) + 6(x + 3)]

= 3(x + 1)(x + 2)(x + 3)

3x² + 13x + 10 = 3x² + 3x + 10x + 10 = 3x(x + 1) + 10(x + 1)

= (x + 1)(3x + 10)

Greatest common divisor = (x + 1)