Question

How do you divide `(- 5+ 16x ^ { 3} + 4x - 8x ^ { 2} ) \div ( 4x ^ { 2} + 1)`?

Answer 1

`4x-2-3/(4x^2+1)`

Explanation:

Using place keeper of no value for ease of alignment.

`color(white)("dddddddddddddd")16x^3-8x^2+4x-5`
`color(magenta)(4x)(4x^2+1)->color(white)(".d") ul(16x^3+0x^2+4x larr" Subtract")`
`color(white)("ddddddddddddddd")0color(white)("d.")-8x^2+0x-5`
`color(magenta)(-2)(4x^2+1)->color(white)("ddddd") ul(-8x^2+0x-2larr" Subtract")`
`color(white)("ddddddddddddddddddddddddddd")color(magenta)(-3) larr" Remainder"`

`color(magenta)( 4x-2-3/(4x^2+1) )`