In each of the following two polynomials, find the value of a, if x+a is a factor:
(i) x3+ax2-2x+a+4
(ii) x4-a2x2+3x-a
(i) Let, f (x) = x3+ax2-2x+a+4 be the given polynomial
From factor theorem,
If (x + a) is a factor of f (x) then f (-a) = 0 [Therefore, x + a = 0, x = -a]
f (-a) = 0
(-a)3 + a (-a)2 - 2 (-a) + a + 4 = 0
- a3 + a3 + 2a + a + 4 = 0
3a + 4 = 0
3a = -4
a = 
Hence, (x + a) is a factor f (x) when a = 
.
(ii) Let, f (x) = x4-a2x2+3x-a be the given polynomial
From factor theorem,
If (x + a) is a factor of f (x) then f (-a) = 0 [Therefore, x + a = 0, x = -a]
f (-a) = 0
(-a)4 – a2 (-a)2 + 3 (-a) - a = 0
a4 – a4 - 3a - a = 0
-4a = 0
a = 0
Hence, (x + a) is a factor f (x) when a = 0.
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