Respuesta :

LammettHash
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

[tex]\dfrac{2p^2+7p-39}{2p-7}=\dfrac12\times\dfrac{2p^2+7p-39}{p-\frac72}[/tex]

Now, carry out the synthetic division:

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

So you have

[tex]\dfrac12\times\dfrac{2p^2+7p-39}{p-\frac72}=\dfrac12\left(2p+14+\dfrac{10}{p-\frac72}\right)=p+7+\dfrac{10}{2p-7}[/tex]

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