How do you evaluate #f(x)=11x^3-6x^2+2# at x=0 using direct substitution and synthetic division?

1 Answer
Jan 30, 2018

Answer:

#f(x) = f(0) = 2#

Synthetic Division
Quotient #color(brown)(= 11x^2 - 6x) #, Remainder #color(red)(= 2/x)#

Explanation:

For x = 0, by Direct Substitution

#f(x) = f(0) = 11 *0 - 6*0 + 2 = 2#

Synthetic Division

#color(white)(aa)0color(white)(aa)|color(white)(aa)11color(white)(aa)-6color(white)(aaa)0color(white)(aaa)2#

#color(white)(aaaaa)|color(white)(aa)darrcolor(white)(aaaa)0color(white)(aaa)0 color(white)(aaa)0#

#color(white)(aaaaa)-----------#

#color(white)(aaaaaaaaa)11color(white)(aa)-6color(white)(aaa)0color(white)(aaa)2#

Quotient #= 11x^2 - 6x #, Remainder #= 2/x#