Question

Find the G.C.D of the polynomials 10x³y³z²​

Answer 1

Step-by-step explanation:

first factorize the given polynomials x3−x2+x−1 and x4−1 as shown below:

x3−x2+x−1=x2(x−1)+1(x−1)=(x−1)(x2+1)

x4−1=(x2)2−(1)2=(x2−1)(x2+1)(∵a2−b2=(a+b)(a−b))=(x−1)(x+1)(x2+1)

The common factors of x3−x2+x−1 and x4−1 are (x−1) and (x2+1), therefore, the GCD is (x−1)(x2+1).

Hence, the greatest common divisor is (x−1)(x2+1).

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Answer 2

Step-by-step explanation:

first factorize the given polynomials x3−x2+x−1 and x4−1 as shown below:

x3−x2+x−1=x2(x−1)+1(x−1)=(x−1)(x2+1)

x4−1=(x2)2−(1)2=(x2−1)(x2+1)(∵a2−b2=(a+b)(a−b))=(x−1)(x+1)(x2+1)

The common factors of x3−x2+x−1 and x4−1 are (x−1) and (x2+1), therefore, the GCD is (x−1)(x2+1).

Hence, the greatest common divisor is (x−1)(x2+1).

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