# In each of the fo

(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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