Question

Factorize x^3 -9x^2 -x +9

Answer 1

answer:- (x-9)(x-1)(x+1)

step by step explanation:-

Factor by grouping

(−9)(2−1)

(x-9)(x^{2}-1)

(−9)(2−+−1)

Factor by grouping

(−9)(2−+−1)

(x-9)({\color{#c92786}{x^{2}-x}}+x-1)

(−9)((−1)+−1)

Factor by grouping

(−9)((−1)+−1)

(x-9)(x(x-1)+x-1)

(−9)(−1)(+1)

Answer 2

Answer:

factors  $( X-9) (X-1)(X+1)$

Step-by-step explanation:

Given    $X^{3} - 9X^{2} - X+9$  

        [  take $X^{2}$ common from $X^{3}$ and $-9X^{2}$  and ($-$) from $-X$ and 9

             $X^{2} ( X} - 9) -(X- 9)$    

      [ take common ($X-9$) from the equation ]

             $( X- 9) ( X^{2} -1)$

here we can write $(X^{2} -1)$ as $(X^{2} - 1^{2} )$

(writing $1=1^{2}$ doesn't change its value )

now expand $(X^{2} -1^{2} )$  using formula $(a^{2} -b^{2} ) = (a+b) (a-b)$

                $(x^{2} -1^{2} ) = (X+1 ) ( X-1)$

 factors of $X^{3} -9X^{2} -X+9$ are $(X-9) ,( X+1) ,( X-1)$

note : make sure that you didn't write directions as i mentioned just write numerical part step by step