The polynomial 9x^5+36x^4+189x^3 in factored form is [tex]-9 x \times x \times x \times(x-7) \times(x+3)[/tex]
Solution:
Given, polynomial equation is [tex]-9 x^{5}+36 x^{4}+189 x^{3}[/tex]
We have to find the factored form of the above given polynomial equation.
Let us solve it by grouping.
Now, take the polynomial ⇒ [tex]-9 x^{5}+36 x^{4}+189 x^{3}[/tex]
By taking common term out, we get
[tex]\rightarrow-9 x^{3}\left(x^{2}-4 x-21\right)[/tex]
[tex]\rightarrow-9 x^{3}\left(x^{2}-(7-3) x-7 \times 3\right)[/tex]
Grouping the terms we get,
[tex]\rightarrow-9 x^{3}\left(\left(x^{2}-7 x\right)+(3 x-7 x^3)\right)[/tex]
Taking common terms out from each group,
[tex]\rightarrow-9 x^{3}(x(x-7)+3(x-7))[/tex]
[tex]\Rightarrow-9 x^{3}((x-7)(x+3))[/tex]
[tex]\rightarrow-9 x \times x \times x \times(x-7) \times(x+3)[/tex]
Thus the factored form of polynomial is found out
