I believe this is a high school level algebra question but if its not please move it.

I am having trouble expanding higher power equations, such as, what steps do i take to solve this?

$\displaystyle 2x^3-4x^2-2x+4=0$

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- Oct 13th 2010, 03:57 PMJuggalomikeseperating higher power variables
I believe this is a high school level algebra question but if its not please move it.

I am having trouble expanding higher power equations, such as, what steps do i take to solve this?

$\displaystyle 2x^3-4x^2-2x+4=0$ - Oct 13th 2010, 04:09 PMyeKciM
$\displaystyle 2x^3-4x^2 -2x +4 = 0$

$\displaystyle 2x^2 (x-2 ) -2 (x-2) =0 $

$\displaystyle (2x^2 -2 ) (x-2) = 0 $

$\displaystyle 2x^2 - 2 = 0 \Rightarrow x^2 = 1 \Rightarrow x_1 = 1 \; x_2 = -1 $

$\displaystyle x-2 = 0 \Rightarrow x_3 = 2 $

$\displaystyle (x-1)(x+1)(x-2) =0 $ - Oct 13th 2010, 06:01 PMJuggalomike
Thanks a lot, didn't think about breaking up the first 2 and the 2nd 2

- Oct 14th 2010, 03:29 AMHallsofIvy
Another way to look at it: the "rational root theorem" says that any

**rational number**roots to a polynomial equation with**integer**coefficients must be of the form $\displaystyle \frac{m}{n}$ with m, the numerator, a divisor of the leading coefficient, and n, the denominator, a divisor of the constant term. Here, the leading coefficent is 2 which has divisors, 1, -1, 2, and -2, and the constant term is 4 which has divisors 1, -1, 2, -2, 4, -4. The only**possible**roots of the equation $\displaystyle 2x^3- 4x^2- 2x+ 4= 0$ are 1, -1, 2, -2, 4, -4, 1/2, -1/2, 1/4, and -1/4. Putting those numbers into the equation, it is easy to see, immediately, that x= 1 is a root and so x- 1 is a factor. We can continue checking or, by "long division" or "synthetic" division, see that $\displaystyle x^2- 4x^2- 2x+ 4= (x- 1)(2x^2- 2x- 4)= 2(x- 1)(x^2- x- 2)$ and then see that the last factors as $\displaystyle (x- 2)(x+ 1)$

(I accidently entered "x^^2" rather than "x^2" but instead of getting a usual error message I got "**blackisted command**". Hope I didn't offend anyone!)