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If f (x)=x^99+ 99x + k is divisible by x + 1 , then k = A. −100 B. −98 C. 98...

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christiano-cr7 | (Level 1) Salutatorian

Posted September 4, 2013 at 5:58 PM via web

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If f (x)=x^99+ 99x + k is divisible by x + 1 , then k =

A. −100

B. −98

C. 98

D. 100

E. 198

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted September 4, 2013 at 6:04 PM (Answer #1)

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`f(x) = x^99 +99x+k`

Using remainder theorem if fully `f(x)` is fully divided by ` (x-a)` then` f(a) = 0` ;

`f(-1) = 0`

`f(-1) = -(1)^99+99(-1)+k = 0`

`-1-99+k = 0`

`K = 100`

So the answer is k = 100. Correct answer is at option D).

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