SOLUTION: Find the constant C such that the denominator will divide evenly into the numerator. 2x^3+9x^2-x+C/x+4 Show the solution.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the constant C such that the denominator will divide evenly into the numerator. 2x^3+9x^2-x+C/x+4 Show the solution.      Log On


   

Question 1186706: Find the constant C such that the denominator will divide evenly into the numerator.
2x^3+9x^2-x+C/x+4
Show the solution.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Study the other one as an example and you will know what to do for this one.

Answer by ikleyn(52877) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the constant C such that the denominator will divide evenly into the numerator.
2x^3+9x^2-x+C/x+4
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The linear binomial (x+4) in the denominator divides the polynomial  f(x) = 2x^3 + 9x^2 - x + C  of the numerator evenly 

if and only if  f(-4) = 0   (the Remainder Theorem).


From condition  f(-4) = 0  find the value of C


    2*(-4)^3 + 9*(-4)^2 - (-4) + C.


It gives


    C = -2*(-4)^3 - 9*(-4)^2 + (-4) = -2*(-64) - 9*16 - 4 = 128 - 144 - 4 = -20



Hence,  C = -20.    ANSWER

Solved.