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Question
Find the HCF of the following pair of polynomials:
a2−1 and 3a−3
a2−1 and 3a−3
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Solution
We know that HCF is the highest common factor.
Factorise a2−1 as follows:
a2−1=(a−1)(a+1) (using identity a2−b2=(a+b)(a−b))
Now, factorise 3a−3 as follows:
3a−3=3(a−1)
Since the common factor between the polynomials a2−1 and 3a−3 is (a−1).
Hence, the HCF is (a−1).
Factorise a2−1 as follows:
a2−1=(a−1)(a+1) (using identity a2−b2=(a+b)(a−b))
Now, factorise 3a−3 as follows:
3a−3=3(a−1)
Since the common factor between the polynomials a2−1 and 3a−3 is (a−1).
Hence, the HCF is (a−1).
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