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Question

Find the HCF of the pair of polynomials using equations:
x33x2+4x12, x4+x3+4x2+4x

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Solution

Factors of x33x2+4x12
=x2(x3)+4(x3)
=(x3)(x+4)
Factors of x4+x3+4x2+4x
=x3(x+1)+4x(x+1)
=(x3+4x)(x+1)
=x(x+4)(x+1)
H.C.F of x33x2+4x12 and x4+x3+4x2+4x
Common factors of (x3)(x+4) and x(x+4)(x+1)
is x+4
H.C.F=x+4

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