Max Value of k for Cubic Polynomial Factoring

[ehrenfest]

Homework Statement

The polynomial P(x) is cubic. What is the largest value of k for which the polynomials Q_1(x) = x^2+(k-29)x-k and Q_2(x) = 2x^2+(2k-43)x+k are both factors of P(x)?

Homework Equations

The Attempt at a Solution

I don't understand the question. How can you determine whether Q_1 and Q_2 are factors of P(x) when they do not tell you what P(x) is!?

 

[cristo]

Presumably you only need to know that it is cubic, so take some general cubic function.

 

[ehrenfest]

How could the answer possibly not depend on what P(x) is? If not, and the answer is greater than 1, that implies that ALL cubic polynomials have a common factor which is absurd!

 

[morphism]

I agree - the wording could have been better. I think what they want you to do is assume that Q_1 and Q_2 are divisors of P, find the values of k for which this is possible, and give them the largest of these values. Using this interpretation, all you need to know about P is that it's a cubic.