Let n2 be an integer and define a polynomial p(x)=x^ n +a_ n-1 x^ n-1 + +a₁ x+a₀ where a ₀, a ₁, a _ n -1 are integers. Suppose we know that np ( x )=(1+ x ) p ^ ( x ) . If b = p (1) , then

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Let n>2 be an integer and define a polynomial p(x)=x^ n +a_ n-1 x^ n-1 + +a₁ x+a₀ where a ₀, a ₁, a _ n -1 are integers. Suppose we know that np ( x )=(1+ x ) p ^ ( x ) . If b = p (1) , then

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Correct answer: C. b is a power of 2

array l n [ x ^ n + a _ n -1 x ^ n -1 + a _ n -2 x ^ n -2 - a ₁ x + a ₀ ] =(1+ x ) ( n x ^ n -1 + a _ n -1 ( n -1) x ^ n -2 . + a _ n -2 x ^ n -3 ( n -2) . + a _ n-3 ( n -3) x ^ n -4 + ) array compare coefficient of x ^ n -1 na _ n -1 =( n -1) a _ n -1 + n Solve a_ n-1 =n or n 1 compare coefficient of x ^ n -2 aligned na _ n -2 &=( n -2) a _ n -2 +( n -1) a _ n -1 a _ n -2 &= n ( n -1) 2 = ^ n C ₂ aligned similarly a_ n-3 = n 3 & So . on aligned b=P(1) &=1+a_ n-1 +a_ n-2 + a₁+a₀ &= n 0+ n 1 + n 2 + . n n =2^ n alig

Let n>2 be an integer and define a polynomial p(x)=x^ n +a_ n-1 x^ n-1 + +a₁ x+a₀ where a ₀, a ₁, a _ n -1 are integers. Suppose we know that np ( x )=(1+ x ) p ^ ( x ) . If b = p (1) , then

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