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Question
Factories:
x3−3x2−9x−5
x3−3x2−9x−5
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Solution
We factorize x3−3x2−9x−5 the given polynomial as shown below:
x3−3x2−9x−5=x3+x2−4x2−4x−5x−5=x2(x+1)−4x(x+1)−5(x+1)=(x+1)(x2−4x−5)=(x+1)(x2−5x+x−5)=(x+1)[x(x−5)+1(x−5)]=(x+1)(x−5)(x+1)=(x−5)(x+1)2
Hence, x3−3x2−9x−5=(x−5)(x+1)2
x3−3x2−9x−5=x3+x2−4x2−4x−5x−5=x2(x+1)−4x(x+1)−5(x+1)=(x+1)(x2−4x−5)=(x+1)(x2−5x+x−5)=(x+1)[x(x−5)+1(x−5)]=(x+1)(x−5)(x+1)=(x−5)(x+1)2
Hence, x3−3x2−9x−5=(x−5)(x+1)2
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