A^3 - 7A - 6 = 0 What is the value of A? And How you Find it? explain it

All possible rational zeros are {±1,2,3,6, and all fractions formed by a combination of the integers)

By inspection using integers first ...

1-7-6=-12 1 is not a root

8-14-6=-12 2 is not a root

27-21-6=0 so 3 is a root so (a-3) is a factor ...

(a^3-7a-6) / (a-3)

a^2 rem 3a^2-7a-6

3a rem 2a-6

2 rem 0 so now we know that we have:

(a-3) (a^2+3a+2) and we can factor the second expression ...

(a-3) (a^2+a+2a+2)

(a-3) (a (a+1) + 2 (a+1))

(a-3) (a+2) (a+1)

So there are three values of a that make the equation true ...

a={-1, - 2, 3}