Question 1186706
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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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<pre>
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.    <U>ANSWER</U>
</pre>

Solved.