Question

factorize x cube +13 x square +32 x +20

Answer 1

Let p (x) = x^3 + 13x^2 +32x + 20
Using hit and trial method
x= -1
p (-1) = -1 + 13 -32 +20
=-33+ 33
= 0
So, (x +1 ) is a factor of p (x) [by factor theorem]
To fing other factors we must divide p (x) by (x+1)
And the other factor found is x^2 +12x + 10
Factorising x^2 +12x +20
= x^2 +10x + 2x +20
= x (x +10) +2 (x +10)
= (x+2)(x+10)
So, polynomial p (x) would be factorised as (x+2)(x +10)(x+1).

Answer 2

look its very simple, questions like this have value of  x satisfying around  1 to 5 but that is not a universal law .