Question

How do you divide `x^3+7x^2-3x+4) div(x+2)` and identify any restrictions on the variable?

Answer 1

`x^2+5x-13+30/(x+2)to(x!=-2)`

Explanation:

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

`"consider the numerator"`

`color(red)(x^2)(x+2)color(magenta)(-2x^2)+7x^2-3x+4`

`=color(red)(x^2)(x+2)color(red)(+5x)(x+2)color(magenta)(-10x)-3x+4`

`=color(red)(x^2)(x+2)color(red)(+5x)(x+2)color(red)(-13)(x+2)color(magenta)(+26)+4`

`=color(red)(x^2)(x+2)color(red)(+5x)(x+2)color(red)(-13)(x+2)+30`

`"quotient "=color(red)(x^2+5x-13)," remainder "=30`

`rArr(x^3+7x^2-3x+4)/(x+2)`

`=x^2+5x-13+30/(x+2)to(x!=-2)`