Question

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

Answer 1

`x-3-2/(x-2)`

Explanation:

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

`"consider the numerator"`

`color(red)(x)(x-2)color(magenta)(+2x)-5x+4`

`=color(red)(x)(x-2)color(red)(-3)(x-2)color(magenta)(-6)+4`

`=color(red)(x)(x-2)color(red)(-3)(x-2)-2`

`"quotient " =color(red)(x-3)," remainder "= -2`

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