Question

When x^4 + ax^2 - 16 is divided by x + 1, the remainder is -14. What is the remainder when x^4 + ax^2 - 16 is divided by x-2?

Answer 1

Answer:

4

Step-by-step explanation:

There is a formula.  if  f(x) is divided by x -r, the remainder is  f(r)

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f(-1) = -14

(-1)^4 + a (-1)^2 - 16 = -14

1 + a - 16 = -14

1 + a = 2

a = 1

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if f(x) =  x^4  +  ax^2  - 16

and  f(x) divided by x - 2

remainder = f(2) =  2^4  + a*2^2 - 16

f(2) = 16 + 4 - 16 = 4