Question

Factorize: `a^2 x^2 + (ax^2 + 1)x + a`

Answer 1

We Multiply x (ax² +1) = ax³ + x

= a² x² + ax³ + x + a

Taking common ax² in (a² x²  + ax³ ) and 1 in ( x + a)

= ax² (a + x) +1( x + a)

= ax² (a + x) +1(a + x)

Taking (a + x ) common in both the terms

= (a + x)(ax² +1)

∴ a² x² + (ax² +1) x + a = (a + x)(ax² +1)