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Assuming you mean a fourth degree polynomial,P4 = x4 + 1P3 = x3 + 1P4*P3 = x7 + x4 + x3 + 1 is a seventh degree polynomial.
x2 - x10 + x5 - x12 - x3
It is a cubic polynomial in x and its value depends on the value of x.
I really want to see x^3 to represent x to the power of 3 and x3 to represent the third element of the sequence (xn). Because in Calculus, we use x3, a5, etc. all the time. Anyway 3x^3 + x + 1 is a degree 3 (highest degree in the poly.) polynomial.
It is not possible to be sure about the answer because there is no sign before the linear term. If the polynomial is x3-4x2+x-4 then, the factors are (x-4) and (x2+1).