SOLUTION: What are all the zeroes for 2x^4 + 13x^3 + 22x^2 + 8x = 0 if -2 is one of the zeroes?

Question 1154821: What are all the zeroes for 2x^4 + 13x^3 + 22x^2 + 8x = 0 if -2 is one of the zeroes?
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!




We can factor out x



Since -2 is one of its zeros, the polynomial in parentheses must be divisible by
(x+2) because (x+2) would have to be one of the factors that you'd have to set
equal to zero in order to get x = -2.  We'll use synthetic division

-2|2 13  22  8  
  |  -4 -18 -8  
   2  9   4  0  

So we have factored the left side of the polynomial equation as



We can factor further as



Use the zero-factor property:

x=0;   x+2=0;    x+4=0;     2x+1=0
         x=-2      x=-4;      2x=-1
                               x=-1/2

The four zeros are 0; -2; -4; -1/2

Edwin

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