How do you divide #(6x^2+41x+31) -: (x+6)#?

2 Answers
Jim G.
Jun 24, 2017

#6x+5+1/(x+6)#

Explanation:

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

#"consider the numerator"#

#color(red)(6x)(x+6)color(magenta)(-36x)+41x+31#

#=color(red)(6x)(x+6)color(red)(+5)(x+6)color(magenta)(-30)+31#

#=color(red)(6x)(x+6)color(red)(+5)(x+6)+1#

#"quotient "=color(red)(6x+5)," remainder "=1#

#rArr(6x^2+41x+31)/(x+6)#

#=(cancel((x+6))(6x+5))/cancel((x+6))+1/(x+6)#

#=6x+5+1/(x+6)#

Tony B · George C.
Jun 24, 2017

#6x+5+1/(x+6)#

Explanation:

#color(white)(?)#

#" "6x^2+41x+31#
#color(white)(?)color(magenta)(+6x)(x+6)->ul(6x^2+36larr" Subtract"#
#" "0+5x+31#
#color(white)(.?)color(magenta)(+5)(x+6)->" "ul(5x+30)larr" Subtract"#
#" "color(magenta)(0+1 larr" Remainder")#

#color(magenta)(6x+5+1/(x+6))#

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