Question

How do you divide `(x ^ { 2} - 9x + 25) \div ( x - 5)`?

Answer 1

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

Explanation:

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

`"consider the numerator"`

`color(red)(x)(x-5)color(magenta)(+5x)-9x+25`

`=color(red)(x)(x-5)color(red)(-4)(x-5)color(magenta)(-20)+25`

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

`"quotient "=color(red)(x-4)," remainder "=5`

`rArr(x^2-9x+25)/(x-5)=x-4+5/(x-5)`