Use synthetic division to determine the quotient and remainder for the division problem. $\left( x ^ { 2 } - 10 x + 8 \right) \div ( x - 9 )$
A) Q: $x + 1$
R: 1
B) Q: $x - 1$
R: 1
C) Q: $x - 1$
$\mathrm { R } : - 1$
D) Q: $x + 1$
$\mathrm { R } : - 1$
E) Q: $x - 1$
R: 0

Question

Quizplus · Accepted Answer

Using synthetic division, we get:

\begin{array}{c|ccccc} \multicolumn{2}{r}{1} & -1 & 10 & \ \cline{2-6} 9 & & 9 & 72 & \ \multicolumn{2}{r}{1} & 8 & \boxed{80} & \end{array}

Therefore, the quotient is $x-1$ and the remainder is $-1$. Choice C is the only one that matches both the quotient and remainder.

Use Synthetic Division to Determine the Quotient and Remainder for the Division