Question

How do you find the quotient of `(x^2+x-20)div(x-4)`?

Answer 1

`x+5`

Explanation:

`color(white)(wwwww)x+5`
`x-4 )bar(x^2+x-20)`
`color(white)(www)ul(color(red)(-)x^2color(red)(+)4x)" "larr` subtract
`color(white)(wwwwwwww)5x-20`
`color(white)(wwn.....ww)color(red)(-)ul(5xcolor(red)(+)20)`
`color(white)(wwwwwwwwwwwwww)0" "` remainder

`(x^2 +x-20) div (x-4) = x+5`

Answer 2

`x+5`

Explanation:

`"factorise the numerator and simplify"`

`rArr(x^2+x-20)/(x-4)`

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

`=x+5larrcolor(red)" quotient"`

Answer 3

Factorise and cancel like factors.

`x+5`

Explanation:

In a division such as `48 div 6`, we could find the quotient by finding factors:

`48/6 = (8 xx 6)/6" "larr` like factors can cancel `" "6/6 =1`

`(8 xx cancel6)/cancel6 = 8`

In the same way we can find the quotient by factorising the numerator:

`(x^2 +x -20)/((x-4)) = ((x+5)(x-4))/((x-4))`

Cancel the like factors:

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

`= x+5`