Using factor theorem, factorize each of the following polynomial:
x4-7x3+9x2+7x-10
Let, f (x) = x4-7x3+9x2+7x-10
The constant term in f (x) is equal to -10 and factors of -10 are 
, 
Putting x = 1 in f (x), we have
f (1) = (1)4 – 7 (1)3 + 9 (1)2 + 7 (1) - 10
= 1 – 7 + 9 + 7 - 10
= 0
Therefore, (x - 1) is a factor of f (x).
Similarly, (x + 1), (x - 2) and (x - 5) are the factors of f (x).
Since, f (x) is a polynomial of degree 4. So, it cannot have more than four linear factors.
Therefore, f (x) = k (x – 1) (x + 1) (x - 2) (x - 5)
x4-7x3+9x2+7x-10 = k (x – 1) (x + 1) (x - 2) (x - 5)
Putting x = 0 on both sides, we get
0 + 0 – 0 - 10 = k (0 – 1) (0 + 1) (0 - 2) (0 - 5)
-10 = -10k
k = 1
Putting k = 1 in f (x) = k (x – 1) (x + 1) (x - 2) (x - 5), we get
f (x) = (x – 1) (x + 1) (x - 2) (x - 5)
Hence,
x4-7x3+9x2+7x-10 = (x – 1) (x + 1) (x - 2) (x - 5)