How do you simplify #\frac { 24x ^ { 3} - 47x ^ { 2} - 69x - 18} { 8x + 3}#?

2 Answers
George C.
Jan 1, 2017

#(24x^3-47x^2-69x-18)/(8x+3)= 3x^2-7x-6#

with exclusion #x != -3/8#

Explanation:

  • Notice that #24x^3# is divisible by #8x#, with quotient #3x^2#.

  • Then #3*3x^2 = 9x^2#, so split the #-47x^2# into #+9x^2-56x^2#.

  • Similarly #-56x^2# is divisible by #8x#, with quotient #-7x#.

  • Then #3*(-7x) = -21x#, so split the #-69x# into #-21x-48x#, etc...

#(24x^3-47x^2-69x-18)/(8x+3)#

#= (24x^3+9x^2-56x^2-21x-48x-18)/(8x+3)#

#= ((24x^3+9x^2)-(56x^2+21x)-(48x+18))/(8x+3)#

#= (3x^2(8x+3)-7x(8x+3)-6(8x+3))/(8x+3)#

#= ((3x^2-7x-6)color(red)(cancel(color(black)((8x+3)))))/color(red)(cancel(color(black)((8x+3))))#

#= 3x^2-7x-6#

with exclusion #x != -3/8#

Barney V.
Jun 4, 2017

#color(green)(3x^2-7x-6#

Explanation:

#(24x^3-47x^2-69x-18)/(8x+3)#

# color(white)(.................)color(green)(3x^2-7x-6#
#color(white)(aa)8x+3##|##overline(24x^3-47x^2-69x-18)#
#color(white)(................)ul(24x^3+9x^2)#
#color(white)(.........................)-56x^2-69x#
#color(white)(...........................)ul(-56x^2-21x)#
#color(white)(......................................)48x-18#
#color(white)(......................................)ul(48x-18)#

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