Question

How do you divide `(4x^4+6x^3+3x-1)/(2x^2+1)`?

Answer 1

`2x^2+3x-1`

Explanation:

`"one way is to use the divisor as a factor in the numerator"`

`"consider the numerator"`

`color(red)(2x^2)(2x^2+1)color(magenta)(-2x^2)+6x^3+3x-1`

`=color(red)(2x^2)(2x^2+1)color(red)(-1)(2x^2+1)color(magenta)(+1)+6x^3+3x-1`

`=color(red)(2x^2)(2x^2+1)color(red)(-1)(2x^2+1)color(red)(+3x)(2x^2+1)color(magenta)(-3x)+3x`

`rArr(4x^4+6x^3+3x-1)/(2x^2+1)`

`=(cancel((2x^2+1))(color(red)(2x^2+3x-1)))/cancel((2x^2+1))`

`=2x^2+3x-1larrcolor(blue)" quotient"`