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Question

If the factorized form of x3+3x29x+5 is (x1)(x2+ax5). Find a

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Solution

x3+3x29x+5=(x+1)(x2+ax5)
Comparing coefficient of each term on LHS and RHS,
x3+3x29x+5=x3+ax25xx2ax+5
=x3+(a1)x2(5+a)x+5
(a1)=3
a=4.
Hence, the answer is 4.

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