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

x³ – 9x² + 23x – 15, 4x² – 16x + 12

x³ – 9x² + 23x – 15

put x = 1 in polynomials equations is 1 – 9(1) + 23 – 15 = 0

This equation is divisible by (x – 1),

then using division algorithm method.

Since,

(x – 1)(x² – 8x + 15) = (x – 1)[x² – 5x – 3x + 15]

= (x – 1)[x(x – 5) – 3(x – 5)] = (x – 1)(x – 3)(x – 5)

4x² – 16x + 12 = 4x² – 12x – 4x + 12 = 4x(x – 3) – 4(x – 3)

= 4(x – 1)(x – 3)

Greatest common divisor = (x – 1)(x – 3) = x² – 4x + 3