Question

factorise:
x^3-3x^2-9x-5​

Answer 1

Answer:

( x + 1 ), ( x - 5 )   and  ( x  + 1 ) are the factors of given polynomial .

Step-by-step explanation:

x^3  -  3x^2  -  9x   -  5

=  x^3 +  x^2  -  4x^2  -  4x  -  5x  -  5

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

=  ( x  +  1 ) . ( x^2 - 4x  - 5 )

=  ( x + 1 ) . ( x^2 - 5x +  x  -  5 )

=  ( x + 1 ) .   { x ( x - 5)  + 1 ( x  -  5 ) }

=  ( x  +   1 ) . ( x  -  5 ) . ( x + 1 )

∴   ( x + 1 ), ( x - 5 )   and  ( x  + 1 ) are the factors of given polynomial .

Answer 2

Step-by-step explanation:

Given Equation is x^3 - 3x^2 - 9x - 5

= > x^3 - 4x^2 + x^2 - 5x - 4x - 5

= > x^3 - 4x^2 - 5x + x^2 - 4x - 5

= > x(x - 4x - 5) + 1(x^2 - 4x - 5)

= > (x + 1)(x^2 - 4x - 5)

= > (x + 1)(x^2 + x - 5x - 5)

= > (x + 1)(x(x + 1) - 5(x + 1))

= > (x + 1)(x + 1)(x - 5)

= > (x + 1)^2(x - 5).

Hope this helps!