Q. 3 A5.0( 1 Vote )

Find the GCD of t

Answer :

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


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