# hi friends,I created a question while i was practicing factorization, but I can't do it

Note by Alpha Beta
5 years, 9 months ago

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You must know the product of the roots and the sum of the roots, you can also use that

- 5 years, 9 months ago

You can use rational root theorem to know if there is a rational root, or you can cyclic factorize it.

- 5 years, 9 months ago

However, there is no rational root

- 5 years, 9 months ago

how do u get this.......

- 5 years, 9 months ago

What of the following techniques do you know how to use to factorize a polynomial?

1. Observation / Trial and Error
3. Remainder Factor Theorem
4. Rational Root Theorem
5. FOIL / Completing the square
6. Cardano's Method

Staff - 5 years, 9 months ago

- 5 years, 9 months ago

For Cardano's method, I'd suggest just reading up on it. It's a bunch of algebra stating how to solve the depressed cubic (no quadratic term).

There is also a general formula for the cubic (and quartic) equation, but I can honestly say that I never bothered to memorize what they are.

Staff - 5 years, 9 months ago

1,2,3,4,5

- 5 years, 9 months ago

- 5 years, 9 months ago

hmmm,,, i'd leave the question if i were you

anyways, you can see solutions here

Click on exact form (its dirty)

- 5 years, 9 months ago

x = -1/6 (1-i sqrt(3)) (27/2-(3 sqrt(69))/2)^(1/3)-((1+i sqrt(3)) (1/2 (9+sqrt(69)))^(1/3))/(2 3^(2/3))

$$x = \frac{-1}{6} (1-i \sqrt{3}) (\frac{\frac{27}{2}-(3 \sqrt{69}}{2})^\frac{1}{3}-(1+i \sqrt{3}) \frac{\frac{1}{2} (9+\sqrt{69})^\frac{1}{3}}{(23^\frac{2}{3})}$$

[LaTex edited in by peter...not sure if I preserved Tim's order's of operations correctly (lots of parentheses), so see his top section for official version]

- 5 years, 9 months ago

Hey Tim,

I don't mean to be intrusive, but I edited in a LaTex attempt of your answer so that people can read it easier. If that is not what you meant, feel free to re-edit it, using my LaTex and the formatting guide for help.

There is a link to the formatting guide at the base of the window where you enter a comment. Please put all math in LaTex as it is way easier to read than teasing out terms bounded by parentheses within parentheses. LaTex is actually easier, or just as hard as typing math the ugly way, but it is still easy to bungle. Please use the edit post button and the preview function, until your math states what you mean. Cheers:)

Staff - 5 years, 9 months ago