Some Proof help, Please!!!?

[toughcookie723]

Could you please help me out with the following proofs :

1. From root theorem: If x=a is a root of a polynomial f(x), then x-a is a factor of f(x), so f(x)=(x-a)g(x), where g(x) is some other polynomial. Use this to prove Hudde's Theorem: f(a)=0 and f'(a)=o if and only if f(x)= (x-a)^2 h(x), where h(x) is some other polynomial.

2. sin x cannot be expressed as a polynomial.

3. Every Integer is either odd or even. (Use division Theorem)

 

[Deleted member 4993]

Could you please help me out with the following proofs :

1. From root theorem: If x=a is a root of a polynomial f(x), then x-a is a factor of f(x), so f(x)=(x-a)g(x), where g(x) is some other polynomial. Use this to prove Hudde's Theorem: f(a)=0 and f'(a)=o if and only if f(x)= (x-a)^2 h(x), where h(x) is some other polynomial.

"If and only if" theorems are proven twice - i.e. - you assume "A" to be true and prove "B" as logical consequence, then assume "B" to be true and prove "A" as logical consequence .,...

2. sin x cannot be expressed as a polynomial.

3. Every Integer is either odd or even. (Use division Theorem)

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