Using synthetic division, what is the quotient and the remainder for polynomial #P(x) = x^3 - 2x^2 - 5x +6# divided by #(x-1)#?

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Answer 1 · 2017-11-20T11:09:34

#(x^2-x-6)#

we need #x^3# so we add #x^2#

#=>#
#(x-1)(x^2#
#=>x^3-x^2#
we need #-2x^2# so we add #-x#

#=>#
#(x-1)(x^2-x#
#=>x^3-x^2-x^2+x#
we need #-5x# so we add #-6#

#=>#
#(x-1)(x^2-x-6#
#x^3-x^2-x^2+x-6x+6#

we have what we need so we can close it

#=>#
#(x-1)(x^2-x-6)#
#x^3-2x^2+5x+6#

#=>#
#(x^3-2x^2+5x+6)/(x-1)=(x^2-x-6)#