Using factor theorem, factorize each of the following polynomial:
x3+2x2-x-2
Let, f (x) = x3+2x2-x-2
The constant term in f (x) is equal to -2 and factors of -2 are 
.
Putting x = 1 in f (x), we have
f (1) = (1)3 + 2 (1)2 – 1 – 2
= 1 + 2 – 1 – 2
= 0
Therefore, (x – 1) is a factor of f (x).
Similarly, (x + 1) and (x + 2) are the factors of f (x).
Since, f (x) is a polynomial of degree 3. So, it cannot have more than three linear factors.
Therefore, f (x) = k (x – 1) (x + 1) (x + 2)
x3+2x2-x-2 = k (x – 1) (x + 1) (x + 2)
Putting x = 0 on both sides, we get
0 + 0 – 0 – 2 = k (0 – 1) (0 + 1) (0 + 2)
-2 = -2k
k = 1
Putting k = 1 in f (x) = k (x – 1) (x + 1) (x + 2), we get
f (x) = (x – 1) (x + 1) (x + 2)
Hence,
x3+2x2-x-2 = (x – 1) (x + 1) (x + 2)
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