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Question

Find the HCF of f(x)=x3+x2x1 and g(x)=x3+x2+x+1

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Solution

We know that HCF is the highest common factor.

Factorise x3+x2x1 as follows:

x3+x2x1=x2(x+1)1(x+1)=(x21)(x+1)=(x1)(x+1)(x+1)=(x1)(x+1)2
(using identity a2b2=(a+b)(ab))

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+x2x1 and x3+x2+x+1 is (x+1).

Hence, the HCF is (x+1).

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