Question

Using long division to find the quotient, what changes do you first

need to make to the dividend (125x3 - 8)?


(125x3 – 8) = (5x – 2)

Answer 1

`(125x^3 - 8)/(5x - 2) = 25x^2 + 10x +4`

Explanation:

Given

`Dividend = 125x^3 - 8`

`Divisor = 5x - 2`

Required

Determine the quotient

See attachment for complete process.

First, divide 125x^3 by 5x

`(125x^3)/(5x) =25x^2`

Write
`25x^2` at the top

Multiply
`5x - 2` by
`25x^2`

`= 125x^3 - 50x^2`

Subtract from 125x^3 - 8

i.e.

`125x^3 - 8 - (125x^3 - 50x^2) = 50x^2 - 8`

Step 2:

Divide 50x^2 by 5x

`(50x^2)/(5x) = 10x`

Write
`10x` at the top

Multiply
`5x - 2` by
`10x`

`= 50x^2 - 20x`

Subtract from 50x^2 - 8

i.e.

`50x^2 - 8 - (50x^2 - 20x) = 20x - 8`

Step 3:

Divide 20x by 5x

`(20x)/(5x) = 4`

Write
`4` at the top

Multiply
`5x - 2` by
`4`

`= 20x - 8`

Subtract from 20x - 8

i.e.

`20x - 8 - (20x - 8) = 0`

Hence:

`(125x^3 - 8)/(5x - 2) = 25x^2 + 10x +4`