Question

$factorise \: x {}^{3 } - 3x {}^{2} - 9x - 5$
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Answer 1

Step-by-step explanation:

x3−3x2−9x−5

= x^3+ x^2 - 4x^2 - 4x - 5x - 5x3+x2−4x2−4x−5x−5

= x^2(x+1) - 4x(x+1) -5(x+1)x2(x+1)−4x(x+1)−5(x+1)

=(x+1)(x^2 - 4x - 5)(x+1)(x2−4x−5)

= (x+1)(x^2- 5x + x - 5)(x+1)(x2−5x+x−5)

= (x+1)[x(x-5) + 1(x-5)](x+1)[x(x−5)+1(x−5)]

 =(x+1)[(x-5)(x+1)](x+1)[(x−5)(x+1)]

 = (x+1)(x+1)(x-5)(x+1)(x+1)(x−5)

 =(x+1)^2(x-5)(x+1)2(x−5)

Hence x^3 - 3x^2 - 9x - 5=(x+1)^2(x-5)x3−3x2−9x−5=(x+1)2(x−5)