How do you find the quotient of (x^2+x-20)div(x-4)(x2+x20)÷(x4)?

3 Answers
Jun 12, 2017

x+5x+5

Explanation:

color(white)(wwwww)x+5wwwwwx+5
x-4 )bar(x^2+x-20)x4)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯x2+x20
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

Jun 12, 2017

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"

Jun 12, 2017

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