Solving for p and q in px^3 + qx^2 - 3x - 7

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To solve for p and q in the polynomial px^3 + qx^2 - 3x - 7, given that (x-1) and (x+1) are factors, one must use the fact that f(1) = 0 and f(-1) = 0. This leads to two simultaneous equations that can be derived by substituting x = 1 and x = -1 into the polynomial. The equations will help determine the values of p and q. The discussion highlights the importance of understanding how to apply the factor theorem in polynomial equations. Assistance is sought for guidance on starting the problem.
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Homework Statement


Given that (x-1) and (x+1) are factors of px^3 + qx^2 - 3x - 7 find the value of of p and q.



Homework Equations


Not sure but I think ou have to solve as simultaneous equations.


The Attempt at a Solution


I am completely lost and have no idea where to start.

Any help would be greatly appreciated. :smile:
 
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Hint: If (x+1) and (x-1) are factors of f(x), then f(-1) = 0 and f(1) = 0.
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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