Let F be a field and f ∈ F [x], a polynomial with coefficients in F . If f can be written as a product of two nonconstant polynomials g, h ∈ F [x], then f is said to be reducible. Otherwise, f is irreducible. For example, the polynomial f(x) = 4x + 12x + 13x + 6x + 1 ∈ Q[x] is reducible since it can be written as f(x) = (4x + 4x + 1)(x + 2x + 1), a product of two polynomials in Q[x]. As we will see below, the polynomial f(x) = x +x +x +x+1 ∈ Q[x] cannot be written as a product of two… Expand

Harold L. Dorwart has taught at Williams College, Washington and Jefferson College, and Trinity College (where he was Seabury professor of mathematics and department chairman (,&UP It 1949-67, dean… Expand