How do you simplify and divide (2c^3-3c^2+3c-4)div(c-2)(2c3−3c2+3c−4)÷(c−2)?

1 Answer
Jim G.
Nov 2, 2017

2c^2+c+5+6/(c-2)2c2+c+5+6c−2

Explanation:

"one way is to use the divisor as a factor in the numerator"one way is to use the divisor as a factor in the numerator

"consider the numerator"consider the numerator

color(red)(2c^2)(c-2)color(magenta)(+4c^2)-3c^2+3c-42c2(c−2)+4c2−3c2+3c−4

=color(red)(2c^2)(c-2)color(red)(+c)(c-2)color(magenta)(+2c)+3c-4=2c2(c−2)+c(c−2)+2c+3c−4

=color(red)(2c^2)(c-2)color(red)(+c)(c-2)color(red)(+5)(c-2)color(magenta)(+10)-4=2c2(c−2)+c(c−2)+5(c−2)+10−4

=color(red)(2c^2)(c-2)color(red)(+c)(c-2)color(red)(+5)(c-2)+6=2c2(c−2)+c(c−2)+5(c−2)+6

"quotient "=color(red)(2c^2+c+5)," remainder "=6quotient =2c2+c+5, remainder =6

rArr(2c^3-3c^2+3c-4)/(c-2)=2c^2+c+5+6/(c-2)⇒2c3−3c2+3c−4c−2=2c2+c+5+6c−2

Related questions
See all questions in Long Division of Polynomials
Impact of this question
2067 views around the world
You can reuse this answer
Creative Commons License