Question 1011718

If x^2 - 3x + 1 is divided by x + 2c, the remainder is -1. What is c? Thank you.
<pre>Since x + 2c is a factor, we can say that: x + 2c = 0 -------> x = - 2c
{{{f(x) = x^2 - 3x + 1}}} --------------- Remainder Theorem
{{{f(- 2c) = (- 2c)^2 - 3(- 2c) + 1 }}} --- Substituting - 2c for x in remainder theorem
{{{- 1 = 4c^2 + 6c + 1}}} -------------- Substituting - 1 for f(- 2c), and simplifying equation
{{{4c^2 + 6c + 1 + 1 = 0}}}
{{{4c^2 + 6c + 2 = 0 }}}
(4c + 2)(c + 1) = 0   
4c + 2 = 0		  OR		  c + 1 = 0
4c = - 2		  OR		  c = 0 – 1
c = {{{(- 2)/4}}}, or {{{highlight_green(c = - 1/2)}}}    OR             {{{highlight_green(c = - 1)}}}