SOLUTION: factor and find all the zeros. one factor has been given f(x)=x^4+5x^3+8x+40; x+5

Algebra ->  Rational-functions -> SOLUTION: factor and find all the zeros. one factor has been given f(x)=x^4+5x^3+8x+40; x+5      Log On


   

Question 1023528: factor and find all the zeros. one factor has been given f(x)=x^4+5x^3+8x+40; x+5
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
-5        |      1       5      8      40
          |
          |             -5      0      -40
          |___________________________________
                 1      0       8      0

First factorization is f%28x%29=%28x%2B5%29%28x%5E3%2B8%29.
You can play with possible factors or roots for the new cubic factor or can use a formula sum of cubes directly.

highlight_green%28f%28x%29=%28x%2B5%29%28x%2B2%29%28x%5E2-2x%2B4%29%29.


Look at the zeros of that quadratic factor.
x=%282%2B-+sqrt%28%28-2%29%5E2-4%2A1%2A4%29%29%2F2
x=%282%2B-+sqrt%28-12%29%29%2F2
x=%282%2B-+i%2A2%2Asqrt%283%29%29%2F2
highlight%28x=1%2B-+i%2Asqrt%283%29%29, and other Real zero is -2.