How do you divide #(x^2 + 7x – 6) / (x-6) # using polynomial long division?

1 Answer
Aug 5, 2018

#(x^2+7x-6)=(x-6)(x+13)+72#

Explanation:

Here ,

Dividend #:color(blue)(x^2+7x-6) and# divisor #: color(red)(x-6#

So ,
#color(white)(..................................)ul(x+13color(white)(.........))larrquotient#
#color(white)(..................)(x-6) # #|# #x^2+7x-6#
#color(white)(......)color(violet)((x-6)*xtocolor(white)(......)ul(x^2-6x)##color(white)(.......)lArr"subtract"#
#color(white)(........................................0)13x-6#
#color(white)(..........)color(violet)((x-6)*13tocolor(white)(.......)ul(13x-78)##color(white)(.......)lArr"subtract"#
#color(white)(....................................................)color(green)(72##color(white)(.........)larr"Remainder"#
Hence ,

#(x^2+7x-6)=(x-6)(x+13)+72#

#Quotient :q(x)=x+13# #"and Remainder " :r(x)=72#