Question

How do you divide `( -x^3+ 4x^2+8x-7 )/(x - 2 )`?

Answer 1

`-x^2+2x+12+17/(x-2)`

Explanation:

One way is to use the divisor as a factor in the numerator.

`color(magenta)"Add / Subtract "" terms incurred as a result"`

`"Consider the numerator"`

`color(red)(-x^2)(x-2)color(magenta)(-2x^2)+4x^2+8x-7`

`=color(red)(-x^2)(x-2)color(red)(+2x)(x-2)color(magenta)(+4x)+8x-7`

`=color(red)(-x^2)(x-2)color(red)(+2x)(x-2)color(red)(+12)(x-2)color(magenta)(+24)-7`

`=color(red)(-x^2)(x-2)color(red)(+2x)(x-2)color(red)(+12)(x-2)+17`

`"quotient "=color(red)(-x^2+2x+12)" remainder "=17`

`rArr(-x^3+4x^2+8x-7)/(x-2)=-x^2+2x+12+17/(x-2)`