How do you evaluate #f(x)=5x^3+4x^2+8x+1# at x=2 using direct substitution and synthetic division?

1 Answer
Jan 30, 2018

Answer:

#f(x) = f(2) = color(red)(73)#

Synthetic Division :
Quotient #color(brown)(Q = 5x^2 + 14x + 36)#, Remainder #color(red)(R = 73 / (x-2)#

Explanation:

Using direct substitution:

#f(x) =color(red)( f(2)) = 5*(2^3) + 4 * (2^2) + (8 * 2) + 1 = 40 + 16 + 16 + 1 = color(red)(73)#

Synthetic Division :

#color(white)(aa)2color(white)(aa)|color(white)(aaa)5color(white)(aaa)4color(white)(aaa)8color(white)(aaa)1#
#color(white)(aaaaaa)|color(white)(a)darrcolor(white)(aa)10color(white)(aa)28color(white)(aa)72#
#color(white)(aaaaaa)--------#
#color(white)(aaaaaaaaaa)5color(white)(aa)14color(white)(aa)36color(white)(aa)73#

Quotient #color(brown)(Q = 5x^2 + 14x + 36)#, Remainder #color(red)(R = 73 / (x-2)#