Question

factorise x cube minus 3 x square - 9 x minus 5

Answer 1

Hii dear friend.....

Here us ur solution =

Question Given x^3 - 3x^2 - 9x - 5

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The factor of 5 are ±1 , ± 5

Let p (x) = x^3 - 3x^2 - 9 x - 5
p ( 5 )=> ( 5 )^3 - 3(5)^2 - 9 (5) - 5
=> 125 - 75 - 45 - 5
=> 5 - 5 = 0
so , x - 5 is a factor of p (x)

If we divide x^3 - 3x^2 - 9x - 5 by x - 5
plzz see pic in the above attachment ....

we get,
=> x^2 + 2x + 1
=> ( x - 5 ) ( x^2 + 2x + 1 )
=> ( x - 5 ) ( x^2 + x + x + 1 )
=> ( x - 5 ) { x ( x + 1 ) + 1 ( x + 1 ) }
=> ( x - 5 ) ( x + 1 ) ( x + 1 ) ans.

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