Question 1186707: Find the constant C such that the denominator will divide evenly into the numerator.
x^4-x^3-3x^2-Cx-3/x-3
Show the solution. Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39620) (Show Source):
You can put this solution on YOUR website! .
Find the constant C such that the denominator will divides evenly into the numerator.
x^4-x^3-3x^2-Cx-3/x-3
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The linear binomial (x-3) in the denominator divides the polynomial f(x) = x^4 - x^3 - 3x^2 - Cx - 3 of the numerator evenly
if and only if f(3) = 0 (the Remainder Theorem).
From condition f(3) = 0 find the value of C
3^4 - 3^3 - 3*3^2 - C*3 - 3 = 0.
It gives
3C = 3^4 - 3^3 - 3*3^2 - 3 = 81 - 27 - 3*9 - 3 = 24.
Hence, C = 24/3 = 8. ANSWERCHECK. f(3) = 3^4 - 3^3 - 3*3^2 - 8*3 - 3 = 81 - 27 - 27 - 24 - 3 = 0.
Solved.
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The response by @josgarithmetic, giving the answer is INCORRECT.
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After my noticing, @josgarithmetic fixed his erroneous answer,
but his calculations (starting from the setup equation) remained INCORRECT.
NEVER trust his solutions; ALWAYS avoid his posts, for your safety.