How do you evaluate #f(x)=2x^3+5x^2+4x+8# at x=-2 using direct substitution and synthetic division?

1 Answer
Oct 25, 2016

Answer:

#f(-2)=4#

Explanation:

#f(x)=2x^3+5x^2+4x+8# at #x=-2#

By direct substitution:

#f(-2)=2(-2)^3+5(-2)^2+4(-2)+8#

#f(-2)=2(-8)+5(4)-8+8#

#f(-2)=color(red)4#

By synthetic division:

#-2|2color(white)(aaaa)5color(white)(aaaaa)4color(white)(aaa)8#
#color(white)(a^2aa)darrcolor(white)a-4color(white)(aa)-2color(white)(a)-4#
#color(white)(aaaa)-------#
#color(white)(aaa^22)2color(white)(a^22aa)1color(white)(aaaa^2)2color(white)(aaa)color(red)4#