Question

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

Answer 1

The polynomial 9x^5+36x^4+189x^3 in factored form is $-9 x \times x \times x \times(x-7) \times(x+3)$

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

$\rightarrow-9 x^{3}\left(x^{2}-4 x-21\right)$

$\rightarrow-9 x^{3}\left(x^{2}-(7-3) x-7 \times 3\right)$

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,

$\rightarrow-9 x^{3}(x(x-7)+3(x-7))$

$\Rightarrow-9 x^{3}((x-7)(x+3))$

$\rightarrow-9 x \times x \times x \times(x-7) \times(x+3)$

Thus the factored form of polynomial is found out