Question

How do you divide `(-7x^3-15x^2-24x-4)/(x-4)`?

Answer 1

`-7x^2-43x-196-788/(x-4)`

Explanation:

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

`"consider the numerator"`

`color(red)(-7x^2)(x-4)color(magenta)(-28x^2)-15x^2-24x-4`

`=color(red)(-7x^2)(x-4)color(red)(-43x)(x-4)color(magenta)(-172x)-24x-4`

`=color(red)(-7x^2)(x-4)color(red)(-43x)(x-4)color(red)(-196)(x-4)color(magenta)(-784)-4`

`=color(red)(-7x^2)(x-4)color(red)(-43x)(x-4)color(red)(-196)(x-4)-788`

`"quotient "=color(red)(-7x^2-43x-196)," remainder "=-788`

`rArr(-7x^3-15x^2-24x-4)/(x-4)`

`=-7x^2-43x-196-788/(x-4)`