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

\[
\begin{array}{r|rrrr}
1 & -2 & -8 & 5 & 2 \\
\hline
& 1 & 0 & \_ & \_ \\
\end{array}
\]

Answer :

Final answer:

In synthetic division, the steps of multiplication and addition are followed using the coefficients of a polynomial. In the provided example, following these steps results in the number -7 in the question mark.

Explanation:

In synthetic division, the number placed in the question mark position is the solution or remainder after division. In your problem, the sequence of numbers represents the coefficients of a polynomial, the number being divided by is 1, and the process of synthetic division will help us find the question mark.

Following the steps of synthetic division:

  1. The first number remains the same (1 becomes 1).
  2. Multiply the first number in the bottom row by the number you're dividing by (1*1=1).
  3. Add the number you just found to the number in the row directly above it and write this sum in the next cell in the bottom row (-2+1=-1).
  4. Repeat steps 2 and 3, continuing to multiply, then add (-1*1=-1, -8+-1=-9).
  5. The same steps are followed until you reach the amount in the question mark.

This method will give you -7 in the question mark after continuing the steps for the rest of the coefficients. So, the answer is -7.

Learn more about Synthetic Division here:

https://brainly.com/question/31409612

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