Question

Synthetic division or polynomial division can not figure this out.

(2p^2+7p-39)/(2p-7)

Answer 1

The basic synthetic division algorithm only applies to quotients like this when the divisor (denominator) is a monic linear polynomial, meaning the coefficient of the leading term needs to be 1.

First write


`(2p^2+7p-39)/(2p-7)=\frac12*(2p^2+7p-39)/(p-\frac72)`

Now, carry out the synthetic division:

...... | 2 ....... 7 ...... -39
7/2 | ....... 7 ...... 49
----------------------------
...... | 2 ...... 14 ...... 10

So you have


`\frac12*(2p^2+7p-39)/(p-\frac72)=\frac12\left(2p+14+(10)/(p-\frac72)\right)=p+7+(10)/(2p-7)`