Given one of the zeros: x = -5 find the other zeros of the polynomial: 2x^3+17x^2+40x+25

Zeros are x={-5, -1, -5/2}

Step-by-step explanation:

In order to do this problem via factoring there are tricks one of which is that you have to try to break things down in either (x+1) or (x-1).  I tried out to get (x+1) first and it worked.  You break numbers down, separate them and factor them and so I obtained:

Since we want to find the zero's meaning roots/x-intercepts y = 0 and so:

For now we'll only focus on the left hand side of the equation and so:

For the last part we can factor this out by first multiplying the outer terms and try to see if any of those factors equal the middle term.  Thus, knowing that 25 × 14 = 350 and that 25+14 = 39 we obtain:

Note that 25 × 2 = 50 and that 10 + 5 = 15 (middle term of the polynomial).

Now we have 3 cases (2x+5)=0 , (x+5)=0 and (x+1)=0.  By solving for x we obtain:

Case 1:

Case 2:

Case 3:

Therefore the zeros for this polynomial are:

x= {-5, -1, -5/2}