Question

Whats the answer for w^5+4w^4+10w^3+40w^2

Answer 1

I'm assuming there's an =0 at the end of this?

You need to factor to get an answer, so:

`w^5+4w^4+10w^3+40w^2=0\\w^4(w+4)+10w^2(w+4)=0\\(w^4+10w^2)(w+4)=0\\w^2(w^2+10)(w+4)=0\\w=0\\w^2+10=0\\w^2=-10\\w=√(-10)=10i\\ w+4=0\\w=-4\\w=0,10i,-4`

If your teacher doesn't want any imaginary numbers, then your answer would be limited to w=0 and 4. (exclude the 10i if you don't want imaginary numbers)

Answer 2

w^2*(w+4)*(w^2+10)

Explanation:

w^5+4w^4+10w^3+40w^2

w^2*(w^3+4w^2+10w+40)\w^2*(w^2*(w+4)+10(w+4))

w^2*(w+4)*(w^2+10)