Question
Factorize:
$a^2x^2 + (ax^2 + 1)x + a$
$a^2x^2 + (ax^2 + 1)x + a$
✓
Answer
$a^2x^2 + (ax^2 + 1)x + a$
We multiply $x(ax^2 + 1) = ax^3 + x = a^2x^2 + ax^3 + x + a$
Taking common $ax^2$ in $(a^2x^2 + ax^3) and 1 in (x + a)$
$= ax^2(a + x) + 1(x + a)$
$= ax^2(a + x) + 1(a + x)$
Taking $(a + x)$ common in both the terms
$= (a + x)(ax^2 + 1)$
$\therefore$ $a^2x^2 + (ax^2+ 1)x + a$
$= (a + x)(ax^2 + 1)$
We multiply $x(ax^2 + 1) = ax^3 + x = a^2x^2 + ax^3 + x + a$
Taking common $ax^2$ in $(a^2x^2 + ax^3) and 1 in (x + a)$
$= ax^2(a + x) + 1(x + a)$
$= ax^2(a + x) + 1(a + x)$
Taking $(a + x)$ common in both the terms
$= (a + x)(ax^2 + 1)$
$\therefore$ $a^2x^2 + (ax^2+ 1)x + a$
$= (a + x)(ax^2 + 1)$
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