How do you use synthetic division to divide #x^4+4x^3+6x^2+4x+1# by #x+1#?

1 Answer
Jul 21, 2018

Answer:

The remainder is #0# and the quotient is #=x^3+3x^2+3x+1#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##-1##|##color(white)(aaaa)##1##color(white)(aaaa)##4##color(white)(aaaaaa)##6##color(white)(aaaa)##4##color(white)(aaaaa)##1#

#color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaa)##-1##color(white)(aaaa)##-3##color(white)(aaa)##-3##color(white)(aaa)##-1#

#color(white)(aaaaaaaaa)###_________

#color(white)(aaaaaaa)##|##color(white)(aaaa)##1##color(white)(aaaa)##3##color(white)(aaaaaa)##3##color(white)(aaaa)##1##color(white)(aaaaa)##color(red)(0)#

The remainder is #0# and the quotient is #=x^3+3x^2+3x+1#

#(x^4+4x^3+6x^2+4x+1)/(x+1)=x^3+3x^2+3x+1#