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

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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) About Me  (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

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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).

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

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

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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(10551) About Me  (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
f%28x%29+=+x%5E2+-+3x+%2B+1 --------------- Remainder Theorem
f%28-+2c%29+=+%28-+2c%29%5E2+-+3%28-+2c%29+%2B+1+ --- Substituting - 2c for x in remainder theorem
-+1+=+4c%5E2+%2B+6c+%2B+1 -------------- Substituting - 1 for f(- 2c), and simplifying equation
4c%5E2+%2B+6c+%2B+1+%2B+1+=+0
4c%5E2+%2B+6c+%2B+2+=+0+
(4c + 2)(c + 1) = 0
4c + 2 = 0 OR c + 1 = 0
4c = - 2 OR c = 0 – 1
c = %28-+2%29%2F4, or highlight_green%28c+=+-+1%2F2%29 OR highlight_green%28c+=+-+1%29