Question

How do you simplify and divide `(2y^3-5h^2+22h)div(2h+3)`?

Answer 1

`h^2-4h+16-48/(2h+3)`

Explanation:

One way is to use the divisor as a factor in the numerator.

`"Consider the numerator"`

`color(red)(h^2)(2h+3)color(magenta)(-3h^2)-5h^2+22h`

`=color(red)(h^2)(2h+3)color(red)(-4h)(2h+3)color(magenta)(+12h)+22h`

`=color(red)(h^2)(2h+3)color(red)(-4h)(2h+3)color(red)(+16)(2h+3)color(magenta)(-48`

`rArr"quotient "=color(red)(h^2-4h+16)" and remainder " =color(magenta)(-48)`

`rArr(2h^3-5h^2+22h)/(2h+3)=h^2-4h+16-48/(2h+3)`