## Intermediate Algebra for College Students (7th Edition)

$x^{2} +3x +1$
$\begin{array}{ccccccccccc} & &x^{2} & +3x & +1 & \\ & &--&--&--&--\\ x+2&) & x^{3} &+5x^{2} &+7x& +2 & \\ & & x^{3}&+2x^{2} & & & \color{red}{\leftarrow \small{x^{2}(x+2) } } \\ & &--&-- & & &\color{red}{ \small{subtract}} \\ & & & 3x^{2} & +7x& +2 & \\ & & & 3x^{2} & +6x & & \color{red}{\leftarrow \small{3x(x+2) } }\\ & & &--&-- & &\color{red}{ \small{subtract}} \\ & & & & x & +2 &\\ & & & & x & +2 & \color{red}{\leftarrow \small{1(x+2) } }\\ & & & &-- &-- & \color{red}{ \small{subtract}} \\ & & & & & 0 \end{array}$ Quotient = $x^{2} +3x +1$ Remainder = $0$. $\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$ $\displaystyle \frac{ x^{3} +5x^{2} +7x +2}{x+2}$ = $x^{2} +3x +1$