Question

the
Find the GCD
polynom
mials
a. 18 (x³- x²+x-1) and 12 (x⁴-1)​

Answer 1

Answer:

Step-by-step explanation:

18(x^3-x^2+x-1) => 6*3 * (x-1)(x^2+1)

12(x^4 - 1) = 6*2 * (x^2+1)(x-1)(x+1)

therefore gcd = 6*(x^2+1)(x-1)

Answer 2

soln: 18(x³-x²+x-1)

= 2×3×3 [ x²(x-1) +1 (x-1) ]

=2×3×3 ( x-1) ( x²+1)

soln: 12 ( x⁴-1)

=2×2×3 (x²)² -1²)

=2×2×3 ( x²+1) ( x²-1²)

=2×2×3 ( x²+1) ( x+1) ( x-1)

Therefore, G.C.D = 2×3 ( x-1) (x²+1)

= 6 ( x-1) ( x²+1)

L.C.M = 6×2×3 ( x-1) ( x+1) ( x²+1)

= 36 ( x-1) ( x+1) ( x²+1)

I hope this will be helpful to everyone who have problem on this question...