Question:
Factorize: \[ a^2x^2+(ax^2+1)x+a \]
Solution:
\[ a^2x^2+(ax^2+1)x+a \]
\[ =a^2x^2+ax^3+x+a \]
\[ =ax(ax+x^2)+1(x+a) \]
\[ =ax(x+a)+1(x+a) \]
\[ =(x+a)(ax+1) \]
\[ \boxed{(x+a)(ax+1)} \]
Factorize: \[ a^2x^2+(ax^2+1)x+a \]
\[ a^2x^2+(ax^2+1)x+a \]
\[ =a^2x^2+ax^3+x+a \]
\[ =ax(ax+x^2)+1(x+a) \]
\[ =ax(x+a)+1(x+a) \]
\[ =(x+a)(ax+1) \]
\[ \boxed{(x+a)(ax+1)} \]