Q. 235.0( 1 Vote )

# If x-2 is

(i) Let, f (x) = x3-2ax2+ax-1 be the given polynomial

From factor theorem,

If (x – 2) is a factor of f (x) then f (2) = 0 [Therefore, x – 2 = 0, x = 2]

f (2) = 0

(2)3 – 2 a (2)2 + a (2) – 1 = 0

8 – 8a + 2a – 1 = 0

7 – 6a = 0

6a = 7

a =

Hence, (x – 2) is a factor of f (x) when a = .

(ii) Let f (x) = x5-3x4-ax3+3ax2+2ax+4 be the given polynomial

From factor theorem,

If (x – 2) is a factor of f (x) then f (2) = 0 [Therefore, x – 2= 0, x = 2]

f (2) = 0

(2)5 – 3 (2)4 – a (2)3 + 3 a (2)2 + 2 a (2) + 4 = 0

32 – 48 – 8a + 12a + 4a + 4 = 0

-12 + 8a = 0

8a = 12

a =

Hence, (x – 2) is a factor of f (x) when a = .

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