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Which of the following represents the divisor and the dividend for the synthetic division problem below?

[tex]
\begin{array}{c|cccc}
2 & 1 & 6 & -16 \\
\end{array}
[/tex]

Answer :

In synthetic division, the number written outside the division symbol represents the zero, [tex]$c$[/tex], from the linear divisor of the form [tex]$x - c$[/tex]. Here, the number is [tex]$2$[/tex], which means that the divisor is

[tex]$$
x-2.
$$[/tex]

The numbers inside the synthetic division tableau, namely [tex]$1$[/tex], [tex]$6$[/tex], and [tex]$-16$[/tex], are the coefficients of the dividend polynomial. They are arranged in order from the highest degree term to the constant term. Therefore, the dividend polynomial is

[tex]$$
1x^2 + 6x - 16 \quad \text{or simply} \quad x^2 + 6x - 16.
$$[/tex]

To summarize:

- The divisor is [tex]$x-2$[/tex].
- The dividend is [tex]$x^2 + 6x - 16$[/tex].

This completes the detailed explanation of the synthetic division setup.

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