Question

if (x-2) is a factor of of x^5-3x^4- ax^3+3ax^2+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:

Answer 2

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.

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Step-by-step explanation: