Question

$if x - 2 is the factor of polynomial x^5 - 3x^4 - ax^3 + 3ax^2 + 2ax + 4 then find the value of a$
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Answer 1

Answer:

Given f(x) = x^5 - 3x^4 - ax^3 + 3ax^2 + 2ax + 4.

Given g(x) = x - 2.

By the remainder theorem, 

x - 2 = 0

x = 2.

Plug x = 2 in f(x), we get

f(2) = (2)^5 - 3(2)^4 - a(2)^3 + 3a(2)^2 + 2a(2) + 4 = 0

      = 32 - 48 - 8a + 12a + 4a + 4 = 0

      = -16 + 4 + 8a = 0

      = -12 + 8a = 0

     8a = 12

      a = 12/8

      a = 3/2.

Therefore the value of a = 3/2.

Step-by-step explanation:

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