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

Remark

Try taking out - 9x^3 to begin with.

-9x^3(x^2 - 4x - 21)

Note 9 goes into 189/9 = 21. You can use a calculator to verify this.  Also note that there is a sign change each term inside the brackets. That comes about because you took out - 9x^3. The minus sign you used needs to be accounted for.

21 only has 2 sets of factors and only 1 set will work. 21 and 1 is 1 set. That couldn't work. The difference is 20. We need a difference of 4.

The other set is 3 and 7. That looks like it could leave 4 as a difference.

x^2 - 4x - 21 would factor as

(x - 7)(x + 3) When you FOIL this, the results are x^2 - 4x - 21.

So the answer is

-9x^3(x - 7)(x + 3)

25

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