Explanation

(b)
Given polynomial is
$(x - 1)(x - 2)(x - 3)\ldots(x - 19)(x - 20)$
$= x^{20} - (1 + 2 + 3 + \ldots + 19 + 20)x^{19}$
+$(1 \times 2 + 2 \times 3 + \ldots + 19 \times 20)x^{18}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ - \ldots + (1 \times 2 \times 3 \times 4 \times \ldots \times 19 \times 20)$
$\therefore$ Coefficient of $x^{19} = - (1 + 2 + 3 +$…+19+20)
$= - \left\lbrack \frac{20}{2}(1 + 20) \right\rbrack$
$= - 10 \times 21 = - 210$