The polynomial can be factorized as the product of two quadratics and one linear polynomial in , all with positive integer leading coefficients. What is the sum of all of the coefficients and constant terms in the three factors?
Given that and are two non-constant polynomials with integer coefficients such that
Details and assumptions
You may use the fact that .
For what constant can the polynomial be factorized into a perfect square of a quadratic in
If the polynomial is factorized as where and are real numbers, what is the value of
Let . How many distinct real roots are there to ?