how to memorize the sum and product of roots for an $n^{th}$ degree equation For my exams I need to know the following equations by heart:

for a polynomial equation: $a_nx+a_{n-1}x^{n-1}+...+a_1x+a_0,$ the sum and product of the roots are given by

$$\textrm{Sum}=-\frac{a_{n-1}}{a_n}$$
$$\textrm{Product}=(-1)^n\frac{a_0}{a_n}.$$

I have never been able to memorize these, and for some reason, they are not on the formula booklet. If anyone has any mnemonic or trick of some sort for memorizing them, it would be very useful to me.

Thank you very much in advance!
Write
$$a_n x^n + a_{n-1}x^{n-1} + ... + a_1 x + a_0 = a_n(x-r_1)...(x-r_n)$$

and develop. You see immediately what is the constant term and the term of degree $n-1$.
Hint:

Write the polynomial as $$(x-r_1)(x-r_2)...(x-r_n),$$ where the roots are $r_1, r_2, ... r_n.$