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Question

Find the HCF of the following pair of polynomials:
x2+2x15 and x27x+12

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Solution

We know that HCF is the highest common factor.

Factorise x2+2x15 as follows:

x2+2x15=x2+5x3x15=x(x+5)3(x+5)=(x3)(x+5)

Now, factorise x27x+12 as follows:

x27x+1=x24x3x+12=x(x4)3(x4)=(x3)(x4)

Since the common factor between the polynomials x2+2x15 and x27x+12 is (x3).

Hence, the HCF is (x3).

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