write a linear factorization of the function:
f(x)=x^3+4x^2+25x+100

Question

write a linear factorization of the function: 
f(x)=x^3+4x^2+25x+100

jhannybean · Answer

$$f(x) = x^3 +4x^2 +25x +100$$Split this function into 2 groups. $$=\color{blue}{(x^3+4x^2)} +\color{red}{(25x+100)}$$Now in each group, factor out the LCM. In this case it would be $\color{blue}{x^2}$ from the first group and $\color{red}{25}$ from the second group.$$=\color{red}{x^2}\color{blue}{(x+4)} +\color{red}{25}\color{blue}{(x+4)}$$You will see that once those are factored out, you have common likes terms as factors. You can combine these. $$f(x)=\color{red}{(x^2+25)}\color{blue}{(x+4)}$$ You will see now that this is the linear factorized form of your function. $$f(x) = x^3 +4x^2 +25x+100 = (x^2+25)(x+4)$$

anonymous · Answer

thank you!

jhannybean · Answer

No problem :) And remember to medal the user that helped you the most! :-)