In the synthetic-division problem shown below, what number belongs in the place of the question mark?

The  number is 0.  

Step-by-step explanation:

The steps to be followed for synthetic-divisions are:

Step 1:

The 1st row is filled with numbers taken from a polynomial equation.

Step 2:

 The 2nd row is to be filled with required numbers to solve the answer row.

Step 3:

Now to fill the second row, just write down the 1st number in the 1st row  in the answer row as it is.

Step 4:

Then the constant (in this problem, it is -2 ) is multiplied with the 1st number in answer row = (1*-2 =-2)

Step 5:

The obtained number is entered in the 2nd row.

Step 6:

Next, do addition of 1st and 2nd row = (-2) + (-2)= -4

Step 7:

Repeat the steps until the end of answer row. (-4*-2= 8) , (-8)+(8)=0 , (0*-2=0) , (5+0= 5)

Solution:

-2| 1  -2  -8  5

        -2   8  0

    1  -4   0  5

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