Theory:

Steps to factorize the cubic polynomial \(p(x)\).
Step 1: Find \(x = a\) where \(p(a) = 0\). That is, we have to find one of the factors.
 
Step 2: Then \(x-a\) is a factor of \(p(x)\).
 
Step 3: Now divide \(p(x)\) by \(x-a\).  That is \(\frac{p(x)}{(x-a)}\).
 
Step 4: Then factorize the quotient(quadratic equation) by splitting its middle term.
Step 1: Let us find one of factors by trial method.
 
Consider the polynomial m3m2+13m13¯.
 
The product of coefficient of \(m^3\) and constant \(=\) \(1 \times -13\) \(=\) \(-13\).
 
We shall now look for the factors of \(-13\).
 
Factors of \(-13\): \(\pm1, \pm13\)
 
Let us start with the first factor \(m = 1\).
 
p(1)=1311+13113p(1)=(1)(1)+1313p(1)=1(1)+1313P(1)=0P(1)=0+0=0
 
So at \(m =1\), p(y)=0.
 
Thus, the factor \(m =1\) satisfies step 1.
 
Step 2:
 
We can conclude that \(m -1\) is a factor of p(k).
 
Step 3: Now divide p(k) by \(m -1\).
 
Let the quotient be \(g(m)\).
 
gm=p(m)m1m2+13m1m3m2+13m13m3m2()(+)¯0+13m1313m13()(+)¯0
 
So, \(g(m) =\) m2+13.
 
p(m)=m1gm=m1m2+13
 
Thus, the factorisation of the cubic polynomial m3m2+13m13 is m1m2+13.