Answer:
The required factors are: x, (x + 6) and (x - 3).
Step-by-step explanation:
As per the question,
The given polynomial is:
[tex]x^{3}+3x^{2}-18x[/tex]
Now,
BY factorization, we get
[tex]x^{3}+3x^{2}-18x[/tex]
[tex]=x(x^{2}+3x-18)[/tex]
By splitting the mid-term, that is split 3x like:
3x = 6x - 3x
Therefore,
[tex]x(x^{2}+6x-3x-18)[/tex]
Now on further solving by taking common factor out, we get
[tex]=x[x(x+6)-3(x+6)][/tex]
[tex]=x(x+6)(x-3)[/tex]
Therefore, the given second polynomial (x - 4), is not a factor of given polynomial [tex]x^{3}+3x^{2}-18x[/tex].
Hence, the given polynomial has three factor x, (x + 6) and (x - 3).
