How do you find the quotient of #(x^2-5x-16)div(x+2)#?

2 Answers
Feb 10, 2017

Answer:

#x-7#

Explanation:

Using the following #color(blue)"algebraic manipulation"#

#"Using the divisor "(x+2)" as a factor in the numerator"#

#(x^2-5x-16)/(x+2)#

#=(color(red)(x)(x+2)+(color(blue)(-2x)-5x)-16)/(x+2)#

#=(color(red)(x)(x+2)color(red)(-7)(x+2)+(color(blue)(+14)-16))/(x+2)#

#=color(red)(x-7)-2/(x+2)#

#rArr"quotient "=x-7#

Feb 10, 2017

Answer:

#x-7=quotient# and remainder #=-2#

Explanation:

# color(white)(aaaaaaaaaa)##x-7#
#color(white)(aaaaaaaaaa)##------#
#color(white)(aaaa)x+4##|##x^2-5x-16##color(white) (aaaa)##∣##color(blue)#
#color(white)(aaaaaaaaaa)##x^2+2x##color(white)#
#color(white)(aaaaaaaaaa)##----#
#color(white)(aaaaaaaaaaa)##0-7x-16#
#color(white)(aaaaaaaaaaaaa)##-7x-14#
#color(white)(aaaaaaaaaaaaaaaaa)##---#
#color(white)(aaaaaaaaaaaaaaaaa)##0-2#

remainder is #=-2# and the quotient is #=x-7#