How to solve or factorize this equation?
$\displaystyle x^4 - x^3 + 8x - 8 = 0$
help please
Hello,
You can observe that the sum of the coefficients is 0. So 1 is solution. This means that you can factorise by (x-1).
So $\displaystyle x^4-x^3+8x-8 = (x-1)Q(x)$
Where Q(x) is a polynom of degree 3 -> Q(x)=ax^3 + bx² + cx + d, with a,b,c,d to determine by developping (x-1)Q(x).
wingless is right. i'd just like to point out that we can solve $\displaystyle x^2 + 8 = 0$ using the sum of two cubes formula (if you don't see the solution immediately). so, $\displaystyle x^3 + 8 = (x + 2)(x^2 - 2x + 2^2) = 0$, and now equate each term in the product to zero and solve.