Question

find the GCD of (x²-x),(x³-x)​

Answer 1

Answer:

We know that HCF is the highest common factor.

Factorise x3+x2−x−1 as follows:

x3+x2−x−1=x2(x+1)−1(x+1)=(x2−1)(x+1)=(x−1)(x+1)(x+1)=(x−1)(x+1)2   

(using identity a2−b2=(a+b)(a−b))    

Now, factorise x3+x2+x+1 as follows:

x3+x2+x+1=x2(x+1)+1(x+1)=(x2+1)(x+1)                   

Since the common factor between the polynomials x3+x2−x−1 and x3+x2+x+1 is (x+1).

Hence, the HCF is (x+1).

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