Question

How do you simplify and divide `(2c^3-3c^2+3c-4)div(c-2)`?

Answer 1

`2c^2+c+5+6/(c-2)`

Explanation:

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

`"consider the numerator"`

`color(red)(2c^2)(c-2)color(magenta)(+4c^2)-3c^2+3c-4`

`=color(red)(2c^2)(c-2)color(red)(+c)(c-2)color(magenta)(+2c)+3c-4`

`=color(red)(2c^2)(c-2)color(red)(+c)(c-2)color(red)(+5)(c-2)color(magenta)(+10)-4`

`=color(red)(2c^2)(c-2)color(red)(+c)(c-2)color(red)(+5)(c-2)+6`

`"quotient "=color(red)(2c^2+c+5)," remainder "=6`

`rArr(2c^3-3c^2+3c-4)/(c-2)=2c^2+c+5+6/(c-2)`