Factorise `18x^(3)-27x^(2)-35x`.

Explanation

`18x^(3)-27x^(2)-35x=x(18x^(2)-27x-35)`
Here, a=18,b=-27,c=-35
`therefore " " axxc=18xx(-35)=-630`
Now, we take two factors of -630 whose sum is -27.
Let two such factors are m and n.
`therefore " " m+n=-27`
and mn=-630
`therefore (m-n)^(2)=(m+n)^(2)-4mn=(-27)^(2)-4(-630)`
`=729+2520=3249=(57)^(2)`
`implies m-n=57`
Adding equations (1) and (3),
2m=30
`implies m=15`
Put this value of m in equation (3).
15+n=-27
`implies n=-42`.
Now, two factors of -630 are -42 and 15.
Now, `18x^(3)-27x^(2)-35x=x[18x^(2)+(-42+15)x-35]=x(18x^(2)-42x+15x-35)`
=x[6x(3x-7)+5(3x-7)]=x(3x-7)(6x+5)