Question

How do you divide `( -3x^3+ 16x^2-24x+9 )/(x + 1 )`?

Answer 1

`-3x^3+16x^2-24x+9` is not divisible by `x+1`

Explanation:

If we descompose `-3x^3+16x^2-24x+9` we obtain:
`(x-3)(-3x^2+7x+3)` which is not divisible by `x+1`.

Answer 2

`-3x^2+19x-43+52/(x+1)`

Explanation:

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

`"consider the numerator"`

`color(red)(-3x^2)(x+1)color(magenta)(+3x^2)+16x^2-24x+9`

`=color(red)(-3x^2)(x+1)color(red)(+19x)(x+1)color(magenta)(-19x)-24x+9`

`=color(red)(-3x^2)(x+1)color(red)(+19x)(x+1)color(red)(-43)(x+1)color(magenta)(+43)+9`

`=color(red)(-3x^2)(x+1)color(red)(+19x)(x+1)color(red)(-43)(x+1)+52`

`"quotient "=color(red)(-3x^2+19x-43)," remainder "=52`

`rArr(-3x^3+16x^2-24x+9)/(x+1)`

`=-3x^2+19x-43+52/(x+1)`