Divide x^3-4x+1 by x-5: Is it Right?

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The discussion centers on the synthetic division of the polynomial x^3 - 4x + 1 by the linear term x - 5. Initial calculations yielded incorrect results, with participants questioning the validity of the answers provided. It is emphasized that the result of dividing a cubic polynomial by a linear term should yield a quadratic polynomial, and the remainder can be found by evaluating the polynomial at x = 5. Participants encourage showing the detailed work to clarify the confusion. Ultimately, the conversation highlights the importance of accurate calculations in polynomial division.
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Divide using synthetic division (x^3-4x+1) / (x-5)

i got x^3 + 1^2 -9 Remainder: 46.

is it right?
 
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Or is it 1x^3 - 9x^2 R: 46

?
 
i think your first answer is correct looking quickly becasue there is a place holder for the x^2 term resulting in 0
 
What am I missing?

You are using synthitic division to divide a cubic by a linear term. Should not your result be a quadratic? None of the suggestions made so far are correct.
 
As integral said it is not right. Why don't you show your work?
 
I might also point out that if you divide a polynomial, P(x), by the linear term x-a, the remainder is P(a). What do you get if you set x= 5 in
x3- 4x+ 1?
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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