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

1 Answer
Jan 31, 2018

Answer:

Quotient #color(blue)(Q = x^2 - 2)#, Remainder #color(blue)(R = 11 / (x + 3))#

Explanation:

Given equation is

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

Substitution

#f(x) = f(3) = -3^3 + (3 * -3^2) - (2*-3) + 5 = 53#

Synthetic Division

#color(white)(aa)-3color(white)(aa)|color(white)(aa)1color(white)(aaaa)3color(white)(aa)-2color(white)(aa)5#
#color(white)(aaaaaaa)|color(white)(aa)darrcolor(white)(a)-3color(white)(aaaa)0color(white)(aa)6#
#color(white)(aaaaaaa)----------#
#color(white)(aaaaaaaaaaaa)1color(white)(aaa)0color(white)(aa)-2color(white)(aa)11#

Quotient #Q = x^2 - 2#, Remainder #R = 11 / (x + 3)#