Let us factorise the following polynomials:
2x3 – x2 + 9x + 5
Given, f(x)= 2x3 – x2 + 9x + 5
In f(x) putting x=±1, 
, ±2, ±3, we see for which value of x, f(x)=0
f(−
)=2.(− 
)3−(−
)2−9.(− 
)+5=0
We observe that f(−
) = 0
From factor theorem, we can say, for (x=−
), (2x+1) is a factor of f(x)
2x3 – x2 + 9x + 5 = 2x3 – x2 + 9x + 5
= 2x3+x2−2x2− x + 10x +5
= x2(2x+1)−x(2x+1)+5(2x+1)
= (2x+1)(x2−x+5)
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