How do you divide #(4x^5 +8x^4 -8x^3 +4x^2 +x-8) / (5x^2 -4x+9)#?

1 Answer
A08
Mar 23, 2016

Since coefficient of highest power of #x#, i.e ., #x^2# term in the denominator is #!=1#, therefore we need to divide using the long division method.
Quotient #=4/5x^3+56/25x^2-156/125x+1396/625#
Remainder#=13229/625x-17564/625#

Explanation:

#color(white)(WWWWWWW)4/5x^3+56/25x^2-156/125x+1396/625#
#5x^2-4x+9)bar(4x^5+8x^4-8x^3+4x^2+x-8)(#
#color(white)(WWWWWW)4x^5-16/5x^4+36/5x^3#
#color(white)(WWWWW)ul(-color(white)(iiW)+color(white)(WiW)-color(white)(WWWWW))#
#color(white)(WWWWWWWWW)56/5x^4-76/5x^3+" "4x^2#
#color(white)(WWWWWWWWW)56/5x^4-224/25x^3+504/25x^2#
#color(white)(WWWWWWWW)ul(-color(white)(WiiW)+color(white)(WiW)-color(white)(WWW))#
#color(white)(WWWWWWWWWWW)-156/25x^3+404/25x^2+x#
#color(white)(WWWWWWWWWWW)-156/25x^3+624/125x^2-1404/125x#
#color(white)(WWWWWWIWW)ul(color(white)(WiiW)+color(white)(WWW)-color(white)(iWW)+)#
#color(white)(WWWWWWWWWWWWW)1396/125x^2+1529/125x-8#
#color(white)(WWWWWWWWWWWWW)1396/125x^2-5584/625x+12564/625#
#color(white)(WWWWWWWiWW)ul(color(white)(WiiW)-color(white)(WWW)+color(white)(WiWW)-)#
#color(white)(WWWWWWWWWWWWWWWWW)13229/625x-17564/625#

Related questions
See all questions in Division of Polynomials
Impact of this question
1508 views around the world
You can reuse this answer
Creative Commons License