How do you divide #(x^3+x+3)/(x-5)#?

3 Answers
Oct 28, 2017

The remainder is #color(red)(133)# and the quotient is #=x^2+5x+26#

Explanation:

Let's perform a synthetic division

#color(white)(aa)##5##color(white)(aaaaa)##|##color(white)(aaa)##1##color(white)(aaaaa)##0##color(white)(aaaaaa)##1##color(white)(aaaaaaaaaa)##3#
#color(white)(aaaaaaaaaaaa)##------------#

#color(white)(aaaa)##color(white)(aaaa)##|##color(white)(aaaa)##color(white)(aaaaa)##5##color(white)(aaaaaa)##25##color(white)(aaaaaaaa)##130#
#color(white)(aaaaaaaaaaaa)##------------#

#color(white)(aaaa)##color(white)(aaaa)##|##color(white)(aaa)##1##color(white)(aaaaa)##5##color(white)(aaaaaa)##26##color(white)(aaaaaaaa)##color(red)(133)#

The remainder is #color(red)(133)# and the quotient is #=x^2+5x+26#

#(x^3+x+3)/(x-5)=x^2+5x+26+133/(x-5)#

Oct 28, 2017

#x^2+5x+26+133/(x-5)#

Explanation:

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

#"consider the numerator"#

#color(red)(x^2)(x-5)color(magenta)(+5x^2)+x+3#

#=color(red)(x^2)(x-5)color(red)(+5x)(x-5)color(magenta)(+25x)+x+3#

#=color(red)(x^2)(x-5)color(red)(+5x)(x-5)color(red)(+26)(x-5)color(magenta)(+130)+3#

#=color(red)(x^2)(x-5)color(red)(+5x)(x-5)color(red)(+26)(x-5)+133#

#"quotient "=color(red)(x^2+5x+26)," remainder" =133#

#rArr(x^3+x+3)/(x-5)=x^2+5x+26+133/(x-5)#

Oct 28, 2017

Quotient#=x^2+5x+26# and remainder#133/(x-5)#

Explanation:

#color(white)(..........)color(white)(.)x^2+5x+26#
#x-5|overline(x^3+0+x+3)#
#color(white)(............)ul(x^3-5x^2)#
#color(white)(......................)5x^2+x#
#color(white)(......................)ul(5x^2-25x)#
#color(white)(..................................)26x+3#
#color(white)(..................................)ul(26x-130)#
#color(white)(................................................)133#

#(x^3+x+3) / (x-5) = x^2+5x+26+133/(x-5)#