Question

How do you simplify and divide `(2b^3+b^2-2b+3)(b+1)^-1`?

Answer 1

`2b^2-b-1+4/(b+1)`

Explanation:

`(2b^3+b^2-2b+3)(b+1)^-1`

`=(2b^3+b^2-2b+3)/(b+1)`

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

`"consider the numerator"`

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

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

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

`=color(red)(2b^2)(b+1)color(red)(-b)(b+1)color(red)(-1)(b+1)+4`

`"quotient "=color(red)(2b^2-b-1)," remainder "=4`

`rArr(2b^3+b^2-2b+3)/(b+1)`

`=2b^2-b-1+4/(b+1)`