How do you evaluate #f(x)=-x^4+8x^3+13x-4# at x=-2 using direct substitution and synthetic division?

1 Answer
Feb 24, 2017

Answer:

The answer is #=-110#

Explanation:

Direct substitution

#f(-2)=-16-64-26-4=-110#

The remainder is #=-110#

We perform a synthetic division

#color(white)(aaaa)##-2##color(white)(aaaa)##|##color(white)(aaaa)##-1##color(white)(aaaa)##8##color(white)(aaaaa)##0##color(white)(aaaaaa)##13##color(white)(aaaa)##-4#

#color(white)(aaaaaa)##color(white)(aaaaa)##|##color(white)(aaa)##color(white)(aaaaaaa)##2##color(white)(aaaaa)##-20##color(white)(aaaa)##40##color(white)(aaaaa)##-106#

#color(white)(aaaaaaaaaa)#------------------------------------------------------------

#color(white)(aaaa)##color(white)(aaaaaa)##color(white)(aaaaaa)##-1##color(white)(aaa)##10##color(white)(aaaaa)##-20##color(white)(aaaaa)##53##color(white)(aaaaa)##color(red)(-110)#

The remainder is #=-110#

The quotient is #=-x^3+10x^2-20x+53#