Question

Solve using long division: ( 2p^2 + 7p - 39) / 2p - 7

Answer 1

Quotient = p + 7

Remainder = 10

Step-by-step explanation

We want to solve by long division:

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

To do this we have:

`\begin{gathered} \text{Divide each term in the polynomial by 2p and multiply by -7:} \\ \text{ p} \\ 2p-7\sqrt[]{2p^2+7p-39} \\ \text{ - (2p}^2\text{ - 7p)} \end{gathered}`

Subtract the lower polynomial from the higher one and repeat the process:

`\begin{gathered} \text{ p + 7} \\ 2p-7\text{ }\sqrt[]{2p^2+7p-39} \\ \text{ - (2p}^2\text{ - 7p) } \\ \Rightarrow14p-39\text{ (-39 is from the original expression)} \\ \text{-(14p - 49) (subtract from the expression above)} \\ \text{ =}>\text{ 10} \end{gathered}`

Therefore, the result of the division is:

Quotient = p + 7

Remainder = 10