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