Chapter 8.4, Problem 20E

(a)

To determine

To prove: The polynomial $1+2x+6x^2-4x^3+2x^4$ is irreducible over the field $\mathbb{Q}$ of rational numbers.

(b)

To determine

To prove: The polynomial $4+9x^2-15x^3+12x^4$ is irreducible over the field $\mathbb{Q}$ of rational numbers.

(c)

To determine

To prove: The polynomial $6-35x+14x^2+7x^5$ is irreducible over the field $\mathbb{Q}$ of rational numbers.

(d)

To determine

To prove: The polynomial $12+22x-55x^2+11x^4+33x^6$ is irreducible over the field $\mathbb{Q}$ of rational numbers.