lets consider p(x) as the product of a linear and a quadratic polynomial the product of the constant terms in both the linear and quadratic polynomials is a positive constant term of p(x) now the factor pairs of 4 are (1,4) or (2,2) and both the factors are either positive or negative so by FACTOR THEOREM p(1) is less than ZERO and hence 1 is not a factor of p(x) 