Question

How do you divide `(4x^4 -5x^2-2x+24)/((x + 4) )`?

Answer 1

`4x^3-16x^2+59x-238+976/(x+4)`

Explanation:

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

`"consider the numerator"`

`color(red)(4x^3)(x+4)color(magenta)(-16x^3)-5x^2-2x+24`

`=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(magenta)(+64x^2)-5x^2-2x+24`

`=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(red)(+59x)(x+4)color(magenta)(-236x)-2x+24`

`=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(red)(+59x)(x+4)color(red)`
`color(white)(=)color(red)(-238)(x+4)color(magenta)(+952)+24`

`"quotient "=color(red)(4x^3-16x^2+59x-238)`

`"remainder "=976`

`rArr(4x^4-5x^2-2x+24)/(x+4)`

`=4x^3-16x^2+59x-238+976/(x+4)`