第1章 1.16

(1)

x4+4=(x2+2)24x2=(x2+2x+2)(x22x+2)x^4 + 4 = (x^2 + 2)^2 - 4x^2 = (x^2 + 2x + 2)(x^2 - 2x + 2)

(2)

a47a2+9=(a23)2a2=(a2a3)(a2+a3)a^4 - 7a^2 + 9 = (a^2 - 3)^2 - a^2 = (a^2 - a - 3)(a^2 + a - 3)

(3)

p4+p2+25=(p2+5)29p2=(p2+3p+5)(p23p+5)p^4 + p^2 + 25 = (p^2 + 5)^2 - 9p^2 = (p^2 + 3p + 5)(p^2 - 3p + 5)

(4)

p413p2q2+4q4=(p22q2)29p2q2=(p2+3pq2q2)(p23pq2q2)p^4 - 13p^2q^2 + 4q^4 = (p^2 - 2q^2)^2 - 9p^2q^2 = (p^2 + 3pq - 2q^2)(p^2 - 3pq - 2q^2)

解説: r31bn1z