Math CentralQuandaries & Queries


Question from Joan, a teacher:

Find all polynomials P(x) satisfying x^2P(x) + P(1-x) = 2x-x^4

Do you have any suggestions?

Hi Joan,

You want the polynomials on the left side and right side to be identical. On the right side the polynomial has degree 4 so the polynomial on the left side must also be of degree 4. Hence the polynomial P(x) must have degree 2 so that x2 P(x) has degree 4. Hence let P(x) = ax2 + bx + c and substitute into the right side. Collect the terms on the left side and you will have an equation of the form

Ex4 + Fx3 + Gx + H = 2x - x4

Thus E = -1, F = 0, G = 2 and H = 0. From these equations you can solve for a, b and c.

If you need further assistance write back.


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