How do you divide (4x^5 +8x^4 -8x^3 +4x^2 +x-8) / (5x^2 -4x+9)4x5+8x4−8x3+4x2+x−85x2−4x+9?

1 Answer
A08
Mar 23, 2016

Since coefficient of highest power of xx, i.e ., x^2x2 term in the denominator is !=1≠1, therefore we need to divide using the long division method.
Quotient =4/5x^3+56/25x^2-156/125x+1396/625=45x3+5625x2−156125x+1396625
Remainder=13229/625x-17564/625=13229625x−17564625

Explanation:

color(white)(WWWWWWW)4/5x^3+56/25x^2-156/125x+1396/625WWWWWWW45x3+5625x2−156125x+1396625
5x^2-4x+9)bar(4x^5+8x^4-8x^3+4x^2+x-8)(5x2−4x+9)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯4x5+8x4−8x3+4x2+x−8(
color(white)(WWWWWW)4x^5-16/5x^4+36/5x^3WWWWWW4x5−165x4+365x3
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

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