Question

How do you divide `( -3x^3+ 6x^2-13x-5 )/(x + 1 )`?

Answer 1

`-3x^2+9x-22+17/(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)+6x^2-13x-5`

`=color(red)(-3x^2)(x+1)color(red)(+9x)(x+1)color(magenta)(-9x)-13x-5`

`=color(red)(-3x^2)(x+1)color(red)(+9x)(x+1)color(red)(-22)(x+1)color(magenta)(+22)-5`

`=color(red)(-3x^2)(x+1)color(red)(+9x)(x+1)color(red)(-22)(x+1)+17`

`"quotient "=color(red)(-3x^2+9x-22)," remainder "=17`

`rArr(-3x^3+6x^2-13x-5)/(x+1)`

`=-3x^2+9x-22+17/(x+1)`