When expressions of the form (x - r) (x - s) are multi-plied out, a quadratic polynomial...

When expressions of the form (x - r) (x - s) are multi-plied out, a quadratic polynomial is obtained. For instance, (x-2)(x-(-7))=(x-2)(x+7)= +5x- 14.

a. What can be said about the coefficients of the polynomial obtained by multiplying out (x - r)(x - s) when both r and s are odd integers? when both r and s are even integers? when one of r and s is even and the other is odd?

b. It follows from part (a) that - 1253x + 255 cannot be written as a product of two polynomials with integer coefficients. Explain why this is so.