How do you evaluate #f(x)=x+1/2x^3# at x=4 using direct substitution and synthetic division?

1 Answer
Jan 30, 2018

Answer:

Direct Substitution : f(x) = f(4) = 36#

Synthetic Division :
Quotient #(1/2)x^2 + 2x + 9#, Remainder # = 18/(x-4)#

Explanation:

For x = 4,

#f(x) = f(4) = (1/2)x^3 + x = (1/2)4^4 + 4 = 36#

Using Synthetic Division,

#color(white)(aa)4color(white)(aa)|color(white)(aa)1/2color(white)(aa)0color(white)(aa)1color(white)(aa)0#
#color(white)(aaaaa)|color(white)(aa)darrcolor(white)(a)2color(white)(aa)8color(white)(aa)18#
#color(white)(aaaaaa)-------#
#color(white)(aaaaaaaaa)1/2color(white)(aa)2color(white)(aa)9color(white)(aa)18#

Quotient #(1/2)x^2 + 2x + 9#, Remainder # = 18/(x-4)#