Divide 2a^3+7a^2-a-2 by 2a+1

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

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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.

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

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