Question

How do you divide `(2x^4+3x^2+12x+5)/(-x^2+3)`?

Answer 1

`-2x^2 - 9 + (12x+32)/(-x^2+3)`

Explanation:

Solve using polynomial long division:

Hope this helps!

Answer 2

`-2x^2-9+(12x+32)/(-x^2+3)`

Explanation:

Using place keepers of no value. Example: `0x^3`

`color(white)("dddddddddd.ddddddd")2x^4+0x^3+3x^2+12x+5`
`color(magenta)(-2x^2)(-x^2+3) ->ul(+2x^4+0x^3-6x^2larr" Subtract")`
`color(white)("dddddddddddddddddd") 0color(white)(".d") +0color(white)("dd")+9x^2+12x+5`
`color(white)(".d")color(magenta)(-9)(-x^2+3)-> color(white)("dddddddd..d")ul(+9x^2+0x-27larr"Sub")`
`color(magenta)(color(white)("ddd")"Remainder "->color(white)("ddddddddddddd")0+12x+32)`

`-2x^2-9+(12x+32)/(-x^2+3)`