>>6
(1)
2(x^2) -4ax +5(a^2)-4x-2a+6
= 2(x^2) -4(a+1)x +5(a^2) -2a+6
= 2(x-(a+1))^2 -2(a+1)^2 +5(a^2) -2a+6
= 2(x-(a+1))^2 +3(a^2) -6a+4

(2)二次式ではない。

(3) a≠0の時
a(x^2) +(2a+1)x +(a-2)
= a(x+((2a+1)/(2a))^2 - (1/4a) (2a+1)^2 +a-2
= a(x+((2a+1)/(2a))^2 - (1/4a) (4(a^2)+4a+1) +a-2
= a(x+((2a+1)/(2a))^2 - (1/4a) -3