Question

How do you divide `(x ^ { 2} - 10x + 9) \div ( x + 5)`?

Answer 1

`x-15+84/(x+5)`

Explanation:

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

Consider the numerator.

`color(red)(x)(x+5)-5x-10x+9`

`=color(red)(x)(x+5)color(red)(-15)(x+5)+75+9`

`=color(red)(x)(x+5)color(red)(-15)(x+5)+84`

`rArr(x^2-10x+9)/(x+5)=color(red)(x-15)+84/(x+5)`

`"That is quotient "=x-15" and remainder "=84`

Answer 2

`x-15+84/(x+5)`

Explanation:

`" "x^2-10x+9`
`color(magenta)(x)(x+5)->ul(x^2+5x) larr" Subtract"`
`" "0-15x+color(white)(.)9`
`color(magenta)(-15)(x+5)->ul(-15x-75) larr" Subtract"`
`" "0color(magenta)(+84 larr" Remainder" )`

`(x^2-10x+9)-:(x+5)" "=" "color(magenta)(x-15+84/(x+5))`