Question

write the polynomial as the product of factors that are irreducible over the rationals
x^4-3x^3-x^2-12x-20

Answer 1

x^4 - 3x^3 - x^2 - 12x - 20 = (x^4 - x^2 - 20) - 3x^3 - 12x

= (x^2 - 5)(x^2 + 4) - 3x(x^2 + 4)

= (x^2 + 4)(x^2 - 4x - 5)

Answer 2

oops, last line should be (x^2 + 4)(x^2 - 3x - 5)