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

x^3= x + 1 factorize........please help me to build my concepts strong.......

#Algebra #HelpMe! #MathProblem

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`2^{34}`	$2^{34}$
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Comments

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

anyways, you can see solutions here

Click on exact form (its dirty)

Harshit Kapur - 8 years, 4 months ago

i want full solution please/........

alpha beta - 8 years, 4 months ago

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

alpha beta - 8 years, 4 months ago

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

Observation / Trial and Error
Quadratic Formula
Remainder Factor Theorem
Rational Root Theorem
FOIL / Completing the square
Cardano's Method

Calvin Lin Staff - 8 years, 4 months ago

Please Calvin,can you teach me CARDANO'S METHOD...........PLEASEEEEEE

alpha beta - 8 years, 4 months ago

@Alpha Beta – 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.

Calvin Lin Staff - 8 years, 4 months ago

1,2,3,4,5

alpha beta - 8 years, 4 months ago

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

Gurpreet Singh - 8 years, 4 months ago

However, there is no rational root

Gurpreet Singh - 8 years, 4 months ago

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

Gurpreet Singh - 8 years, 4 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]

Tim Ye - 8 years, 4 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:)

Peter Taylor Staff - 8 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$