Question

How do you divide `(-2x^3-23x^2-4x+11)/(x-5)`?

Answer 1

`-2x^2-33x-169-834/(x-5)`

Explanation:

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

`"consider the numerator"`

`color(red)(-2x^2)(x-5)color(magenta)(-10x^2)-23x^2-4x+11`

`=color(red)(-2x^2)(x-5)color(red)(-33x)(x-5)color(magenta)(-165x)-4x+11`

`=color(red)(-2x^2)(x-5)color(red)(-33x)(x-5)color(red)(-169)(x-5)color(magenta)(-845)+11`

`=color(red)(-2x^2)(x-5)color(red)(-33x)(x-5)color(red)(-169)(x-5)-834`

`"quotient "=color(red)(-2x^2-33x-169)," remainder "=-834`

`rArr(-2x^3-23x^2-4x+11)/(x-5)`

`=-2x^3-33x-169-834/(x-5)`