P.S. I did it on paperPolynomial Division: 3x^3-5x^2+10x+4 / 3x+1

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The discussion focuses on using polynomial long division to divide the polynomial 3x^3 - 5x^2 + 10x + 4 by 3x + 1. An initial attempt at the solution was shared, but there was confusion regarding the notation and the final answer. The correct quotient derived from the division is x^2 - 2x + 4. Participants clarified the relationship between division and multiplication in polynomial equations. The conversation highlights the importance of clear notation in mathematical solutions.
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Homework Statement


Use polynomial long division to determine the quotient when

3x^3-5x^2+10x+4 divided by 3x+1

The Attempt at a Solution



Please see attachment as I wasn't quite sure how to write my answer here
:shy:
 

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If A / B = C, then does that mean that A * C = B? That's what you have written at the bottom.
 
SteamKing said:
If A / B = C, then does that mean that A * C = B? That's what you have written at the bottom.

Oops should be

3x^3+5x^2+10x+4/3x+1=x^2-2x+4

I think..
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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