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

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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) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E4+%2B+13x%5E3+%2B+22x%5E2+%2B+8x+=+0

We can factor out x

x%282x%5E3+%2B+13x%5E2+%2B+22x+%2B+8%29+=+0

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

x%28x%2B2%29%282x%5E2+%2B+9x+%2B+4%29+=+0

We can factor further as

x%28x%2B2%29%28x%2B4%29%282x%2B1%29=0

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