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Question

Find the HCF of p(x)=(x327)(x23x+2) and q(x)=(x2+3x+9)(x25x+6).

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Solution

Given : p(x)=(x327)(x23x+2) and q(x)=(x2+3x+9)(x25x+6).
Now, p(x)=(x327)(x23x+2)
=(x333)(x22xx+2)
=(x3)(x2+3x+9)(x2)(x1) ........ [Using formula of (a3b3)]
Also, q(x)=(x2+3x+9)(x25x+6)
=(x2+3x+9)(x23x2x+6)
=(x2+3x+9)(x2)(x3)
The common factors in p(x) and q(x) are (x3),(x2) and (x2+3x+9)
Thus, the HCF of p(x) and q(x) is (x2)(x3)(x2+3x+9)

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