SOLUTION: Given the polynomial P(x)=2x^3-x^2-13x-6 and one of its factors:x+2. How many zeros will there be. How would you know that? Find the remaining factors of the polynomial. please

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Question 427006: Given the polynomial P(x)=2x^3-x^2-13x-6 and one of its factors:x+2.
How many zeros will there be. How would you know that?
Find the remaining factors of the polynomial.
please explain how you found the others.

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
There are three zeros, since it's a third degree polynomial (fundamental theorem of algebra).

Divide P%28x%29+=+%282x%5E3+-+x%5E2+-+13x+-+6%29%2F%28x%2B2%29 using either long or synthetic division. You should obtain 2x%5E2+-+5x+-+3. We find the other zeros of the function using the quadratic equation:

x+=+%285+%2B-+sqrt%2825+%2B+24%29%29%2F4+=+%285+%2B-+7%29%2F4 = 3 or -1/2. Hence, this polynomial factors to %28x-3%29%28x%2B1%2F2%29 and P(x) is equal to %28x-3%29%28x%2B1%2F2%29%28x%2B2%29.