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Question
Find the HCF of the following pair of polynomials:
m2−3m+2 and m2+m−6
m2−3m+2 and m2+m−6
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Solution
We know that HCF is the highest common factor.
Factorise m2−3m+2 as follows:
m2−3m+2=m2−2m−m+2=m(m−2)−1(m−2)=(m−1)(m−2)
Now, factorise m2+m−6 as follows:
m2+m−6=m2+3m−2m−6=m(m+3)−2(m+3)=(m−2)(m+3)
Since the common factor between the polynomials m2−3m+2 and m2+m−6 is (m−2).
Hence, the HCF is (m−2).
Factorise m2−3m+2 as follows:
m2−3m+2=m2−2m−m+2=m(m−2)−1(m−2)=(m−1)(m−2)
Now, factorise m2+m−6 as follows:
m2+m−6=m2+3m−2m−6=m(m+3)−2(m+3)=(m−2)(m+3)
Since the common factor between the polynomials m2−3m+2 and m2+m−6 is (m−2).
Hence, the HCF is (m−2).
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