Explanation

(d)
$x^{12} - x^{9} + x^{4} - x + 1 > 0$
When $0 < x < 1;x^{4} > x^{9}\$and$\ 1 > x$
$\therefore x^{12} + \left( x^{4} - x^{9} \right) + (1 - x) > 0$
$\Rightarrow \$Positive for all $x$
Again, when $x > 1:$
$x^{12} - x^{9} + x^{4} - x + 1 > 0$
$\therefore\$Largest interval $(0,\infty),$ also the above inequality is true for $x < 0$