How do you find the quotient of #(c^3-27)div(c-3)#?

2 Answers
Mar 28, 2017

Answer:

#c^2 + 3 c + 9#

Explanation:

we use a long division to solve it.

# c^3 -27 # #--->c^2 * (c -3)#
#-(c^3 - 3 c^2)#
.................................
#3 c^2 - 27# #---> 3 c * (c -3)#
#-(3 c^2 - 9 c)#
.................................
#9 c - 27# #---> 9 * (c -3)#
#-(9 c - 27)#
...............................
#0#

the answer is #c^2 + 3 c + 9#

Mar 28, 2017

Answer:

#c^2+3c+9#

Explanation:

The numerator is a #color(blue)"difference of cubes"# and in general is factorised as shown.

#color(red)(bar(ul(|color(white)(2/2)color(black)(a^3-b^3=(a-b)(a^2+ab+b^2))color(white)(2/2)|)))#

#c^3-27=(c)^3-(3)^3rArra=c" and " b=3#

#rArrc^3-27=(c-3)(c^2+3c+9)#

#rArr(c^3-27)/(c-3)=(cancel((c-3)^1)(c^2+3c+9))/(cancel((c-3)^1)#

#=c^2+3c+9larrcolor(red)" quotient"#