what is hit and trial method .

Hit and trial method is used to find the factors / roots of the given polynomial of degree more than 2.

In this method, we put some value in the given polynomial and if it satisfies the given polynomial, then it is the zero of that polynomial.

Suppose that given polynomial is

$p (x) = x^{3} + 13 x^{2} + 32 x + 20$

We see that x = –1 is a zero of p(x) as

$p (- 1) = - 1 + 13 - 32 + 20 = 0$

∴ x = –1 is a zero of p(x).

⇒ (x + 1) is a factor of p(x).

Thus, we can write p(x) as

$p (x) = (x + 1) (x^{2} + 12 x + 20)$

Again you can factorize (x² + 12x + 20) using hit and trial or by splitting middle term.