1. ## Factorization

$\displaystyle D^5-13D^3+26D^2+82D+104=0$

2. Find the positive and negative factors of $\displaystyle 104$.

Then substitute each of these into the polynomial.

If any of them (call it $\displaystyle a$) gives you $\displaystyle 0$ after simplifying the left hand side, then $\displaystyle (x - a)$ is a factor.

After you've done that, long divide, follow the same process.

3. Originally Posted by Prove It
Find the positive and negative factors of $\displaystyle 104$.

Then substitute each of these into the polynomial.

If any of them (call it $\displaystyle a$) gives you $\displaystyle 0$ after simplifying the left hand side, then $\displaystyle (x - a)$ is a factor.

After you've done that, long divide, follow the same process.
I found a factor $\displaystyle D+4$, but I can not find the facors of other factor $\displaystyle D^4-4D^3+3D^2+14D+26$.

4. Hint : plot your polynomial and have a look at it. Then you should understand why you can't find other factors

5. You've found the only real root of f(x)=0.