# How do you use synthetic division to divide 16x^3+8x^2-40x-115 divided by 2x-5?

$\frac{16 {x}^{3} + 8 {x}^{2} - 40 x - 115}{2 x - 5} = 8 {x}^{2} + 24 x + 40 + \frac{85}{2 x - 5}$

#### Explanation:

Use the coefficient 2 of the divisor to transform first the dividend so that

$\frac{16 {x}^{3} + 8 {x}^{2} - 40 x - 115}{2 x - 5} = \frac{8 {x}^{3} + 4 {x}^{2} - 20 x - \frac{115}{2}}{x - \frac{5}{2}}$

Now, use synthetic division

The degree of the terms are already arranged so,

$\text{ "8 " " " 4 " " " -20 " " "-115/2" " " }$$| \underline{\text{ " } \frac{5}{2}}$
$\underline{\text{ " " " " "20" " " " "60" " " " } 100}$
$\text{ "8" " " "24" " " "40" " " "85/2" " } \leftarrow$the remainder

$8 {x}^{2} + 24 x + 40 + \frac{\frac{85}{2}}{x - \frac{5}{2}}$
$8 {x}^{2} + 24 x + 40 + \frac{85}{2 x - 5}$