Use the factor theorem to determine if the given binomial is a factor of $$ f(x) $$. $$ f(x)=x^{4}-2401 $$ (a) $$ x-7 $$ (b) $$ x+7 $$

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1. **Recall the Factor Theorem:**  
   The factor theorem states that a binomial $$ x - c $$ is a factor of a polynomial $$ f(x) $$ if and only if $$ f(c) = 0 $$.

2. **For (a) $$ x-7 $$:**  
   Evaluate $$ f(7) $$.  
   $$
   f(7) = 7^4 - 2401
   $$
   Compute $$ 7^4 $$:
   $$
   7^4 = 2401
   $$
   So,  
   $$
   f(7) = 2401 - 2401 = 0
   $$
   Since $$ f(7)=0 $$, by the factor theorem, $$ x-7 $$ is a factor of $$ f(x) $$.

3. **For (b) $$ x+7 $$:**  
   Write $$ x+7 $$ in the form $$ x-(-7) $$. We need to evaluate $$ f(-7) $$.  
   $$
   f(-7) = (-7)^4 - 2401
   $$
   Compute $$ (-7)^4 $$:  
   $$
   (-7)^4 = 2401
   $$
   Therefore,  
   $$
   f(-7) = 2401 - 2401 = 0
   $$
   Since $$ f(-7)=0 $$, by the factor theorem, $$ x+7 $$ is also a factor of $$ f(x) $$.

4. **Conclusion:**  
   Both $$ x-7 $$ and $$ x+7 $$ are factors of $$ f(x)=x^4-2401 $$.
$$ x-7 $$ and $$ x+7 $$ are both factors of $$ f(x) = x^4 - 2401 $$.

Use the factor theorem to determine if the given binomial is a factor of \( f(x) \). \( f(x)=x^{4}-2401 \) (a) \( x-7 \) (b) \( x+7 \)

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