Question

Rewrite the polynomial-9x^5+36x^4+189x^3 in factored form, using the factoring method method you prefer.

Answer 1

The answer is -9x^3(x - 7) (x+3)

Answer 2

The polynomial 9x^5+36x^4+189x^3 in factored form is
`-9 x * x * x *(x-7) *(x+3)`

Solution:

Given, polynomial equation is
`-9 x^(5)+36 x^(4)+189 x^(3)`

We have to find the factored form of the above given polynomial equation.

Let us solve it by grouping.

Now, take the polynomial ⇒
`-9 x^(5)+36 x^(4)+189 x^(3)`

By taking common term out, we get

`\rightarrow-9 x^(3)\left(x^(2)-4 x-21\right)`

`\rightarrow-9 x^(3)\left(x^(2)-(7-3) x-7 * 3\right)`

Grouping the terms we get,

`\rightarrow-9 x^(3)\left(\left(x^(2)-7 x\right)+(3 x-7 x^3)\right)`

Taking common terms out from each group,

`\rightarrow-9 x^(3)(x(x-7)+3(x-7))`

`\Rightarrow-9 x^(3)((x-7)(x+3))`

`\rightarrow-9 x * x * x *(x-7) *(x+3)`

Thus the factored form of polynomial is found out