If one zero of polynomial 2x^3+x^2-7x-6 is 2 then find all zeroes

2,-1 and - 3/2

Step-by-step explanation:

If one zero of polynom is 2 then we can divide our polinom with (x-2), and we will get

(2x^3+x^2-7x-6) / (x-2) = 2x^2+5x+3

Now we have ti find zeros for 2x^2+5x+3

3 is without x so we have factors:

1,-1,3,-3, 1/2,-1/2,3/2,-3/2.

Chack does any of them zero.

For - 1 we have:

2 (-1) ^2+5 (-1) + 3=2-5+3=0

So - 1 is zero of the polynom.

Now divide again with (x+1) wi get:

(2x^2+5x+3) / (x+1) = 2x+3

2x+3=0 if x=-3/2

So we have all zeros:

2,-1 and - 3/2