Question

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

Answer 1

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

Explanation:

One way is to use the divisor x - 2 as a factor in the numerator.

`"Consider the numerator"`

`color(red)(x^2)(x-2)color(red)(+2x^2)+2x^2-3x-5`

`=color(red)(x^2)(x-2)color(red)(+4x)(x-2)color(red)(+8x)-3x-5`

`=color(red)(x^2)(x-2)color(red)(+4x)(x-2)color(red)(+5)(x-2)color(red)(+10)-5`

`=color(red)(x^2)(x-2)color(red)(+4x)(x-2)color(red)(+5)(x-2)+5`

`rArr(x^3+2x^2-3x-5)/(x-2)=color(red)(x^2+4x+5)+5/(x-2)`

`"quotient is " x^2+4x+5" and remainder " =5`