Synthetic division question Why does the answer to (x^3 +3x^2+11x+9)/(x+1) not have a fraction under it...  (x^2+2x+9) But (2x^4-x^3-7x^2+7x+10)/(x-2) have a fraction?  2x^3…

Question

Synthetic division question

Why does the answer to
`(x^3 +3x^2+11x+9)/(x+1)` not have a fraction under it... 
`(x^2+2x+9)`
But
`(2x^4-x^3-7x^2+7x+10)/(x-2)` have a fraction? 
`2x^3+3x^2-1x+5+ (25)/(x-2)`

Answer 1

`\bf \cfrac{2x^4-x^3-7x^2+7x+10}{x-2}\\\\ -----------------------------\\\\ \begin{array}{llrrrrrrr} 2&|&2&-1&-7&7&10\\ &|&&4&6&-2&10\\ --&--&--&--&--&--&--&\\ &&2&3&-1&5&\boxed{20}&\leftarrow \textit{remainder} \end{array}\\\\ -----------------------------\\\\ 2x^3+3x^2-1x+5+\boxed{(20)/(x-2)}`