Question

How do you long divide `(8x^3+12x^2+6x+5) / (2x+1)`?

Answer 1

`(8x^3+12x^2+6x+5)/(2x+1)=4x^2+4x+1+4/(2x+1)`

Explanation:

Solution:

Arrange the dividend and divisor so that their degree of terms are sorted from highest degree to the lowest degree.

`" " " " " "underline(4x^2+4x+1" " " " " " " ")`
`2x+1 |~8x^3+12x^2+6x+5`
`" " " " " "underline(8x^3+4x^2" " " " " " " ")`
`" " " " " " " " " " "+8x^2+6x+5`
`" " " " " " " " " " underline(+8x^2+4x" " " " ")`
`" " " " " " " " " " " " " " " "2x+5`
`" " " " " " " " " " " " " " " "underline(2x+1)`
`" " " " " " " " " " " " " " " " " " " " "4`

Write the answer

`("Dividend")/("Divisor")="Quotient"+("Remainder")/("Divisor")`

`(8x^3+12x^2+6x+5)/(2x+1)=4x^2+4x+1+4/(2x+1)`

God bless....I hope the explanation is useful.