How do you divide #( 3x ^ { 3} + 11x ^ { 2} + 4x + 1) \div ( x ^ { 2} + x )#?

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Answer 1 · 2017-11-03T09:28:35

The remainder is #=-4X+1# and the quotient is #=3X+8#

#A=BQ+R#

#Q=# is the quotient

#R# is the remainder

Degree of #R# is #<# the degree of #B#

#A=3X^3+11X^2+4X+1#

#B=X^2+X#

Perform a long division

#color(white)(aaaa)##3X^3+11X^2+4X+1##color(white)(aaaa)##|##X^2+X#

#color(white)(aaaa)##3X^3+3X^2##color(white)(aaaaaaaaaaaaaa)##|##3X+8#

#color(white)(aaaa)##0X^3+8X^2+4X#

#color(white)(aaaaaaaaaa)##8X^2+8X#

#color(white)(aaaaaaaaaa)##0X^2-4X+1#

Therefore,

The remainder is #=-4X+1# and the quotient is #=3X+8#

#(3X^3+11X^2+4X+1)/(X^2+X)=(3X+8)+(-4X+1)/(X^2+X)#