SOLUTION: If x^2 - 3x + 1 is divided by x + 2c, the remainder is -1. What is c? Thank you.

Question 1011718: If x^2 - 3x + 1 is divided by x + 2c, the remainder is -1. What is c? Thank you.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you can solve this by synthetic division or by long division.
see the following worksheet:

first workssheet divides using long division and using synthetic division.

the remainder is 4c^2 + 6c + 1
since the remainder is -1, you set 4c^2 + 6x + 1 equal to -1 and then solve for c.

you add 1 to both sides of the equation to get 4c^2 + 6x + 2 = 0

then you factor.

the second worksheet shows you the result of factoring 4c^2 + 6x + 2 = 0

the factored equation is (4c+2) * (c+1) = 0.

solve for c to get c = -1/2 or c = -1

this means that 2c = -1 or 2c = -2

those are the roots of the quadratic equation.

when 2c = -1, x + 2c = x - 1.

when 2c = -2, x + 2c = x - 2.

your divisors of x^2 - 3x + 1 are (x-1) and (x-2).

the next worksheet shows you long division by x-1 and by x-2.

the next worksheet shows you synthetic division by x-1 and by x-2.

if you need a lesson on how to do long division or how to do synthetic division or how to factor a quadratic, see the following refences.

http://www.purplemath.com/modules/factquad.htm

http://www.purplemath.com/modules/polydiv2.htm

http://www.purplemath.com/modules/synthdiv.htm

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

If x^2 - 3x + 1 is divided by x + 2c, the remainder is -1. What is c? Thank you.

Since x + 2c is a factor, we can say that: x + 2c = 0 -------> x = - 2c
--------------- Remainder Theorem
--- Substituting - 2c for x in remainder theorem
-------------- Substituting - 1 for f(- 2c), and simplifying equation

(4c + 2)(c + 1) = 0
4c + 2 = 0 OR c + 1 = 0
4c = - 2 OR c = 0 � 1
c = , or OR
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