You need to write the division symbol such that:

`a^2`

_______________

2a+1)`2a^3+7a^2-a-2 `

Notice that dividing `2a^3` by 2a yields `a^2` .

You need to multiply `a^2` by 2a + 1 and the result needs to be set under `2a^3+7a^2-a-2 ` such that:

`a^2`

_______________

2a+1)`2a^3+7a^2-a-2`

`2a^3 + a^2`

...

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You need to write the division symbol such that:

`a^2`

_______________

2a+1)`2a^3+7a^2-a-2 `

Notice that dividing `2a^3` by 2a yields `a^2` .

You need to multiply `a^2` by 2a + 1 and the result needs to be set under `2a^3+7a^2-a-2 ` such that:

`a^2`

_______________

2a+1)`2a^3+7a^2-a-2`

`2a^3 + a^2`

You need to subtract `2a^3 + a^2` from `2a^3+7a^2-a-2` such that:

`a^2`

_______________

2a+1)`2a^3+7a^2-a-2`

-`2a^3 - a^2`

________________

// `6a^2`

You need to remember that you need to carry down the next term from dividend such that:

` a^2`

_______________

`2a+1)2a^3+7a^2-a-2`

` -2a^3 - a^2`

________________

//` 6a^2 - a`

You need to divide `6a^2` by 2a such that:

` a^2 + 3a - 2`

_______________

`2a+1` `)` `2a^3+7a^2-a-2`

` -2a^3 - a^2`

________________

// `6a^2 - a`

-`6a^2 - 3a`

_______________

// `-4a - 2`

` 4a + 2`

_____________

// //

**Hence, notice that 2a+1 divides exactly the polynomial `2a^3+7a^2-a-2, ` hence, the quotient is `a^2 + 3a - 2` and reminder is 0.**

Using synthetic division 2a^3+7a^2-a-2 has to be divided by 2a+1

2a + 1 | 2a^3 + 7a^2 - a - 2 | a^2 + 3a - 2

.............2a^3 + a^2

------------------------------------------

.........................6a^2 - a - 2

.........................6a^2 + 3a

------------------------------------------

..................................-4a - 2

..................................-4a - 2

--------------------------------------------

.......................................0

**The result of 2a^3+7a^2-a-2 divided by 2a+1 is a^2 + 3a - 2**