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If p(x)=x+9 then find p(x)+p(-x)....

If `p(x)=x+9` then find p(x)+p(-x).

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To solve the problem, we need to find \( p(x) + p(-x) \) given that \( p(x) = x + 9 \). ### Step-by-Step Solution: 1. **Identify \( p(x) \)**: We know that \( p(x) = x + 9 \). 2. **Find \( p(-x) \)**: To find \( p(-x) \), we substitute \(-x\) into the polynomial: \[ p(-x) = -x + 9 \] 3. **Add \( p(x) \) and \( p(-x) \)**: Now we will add \( p(x) \) and \( p(-x) \): \[ p(x) + p(-x) = (x + 9) + (-x + 9) \] 4. **Simplify the expression**: Combine like terms: \[ p(x) + p(-x) = x - x + 9 + 9 \] The \( x \) and \(-x\) cancel each other out: \[ = 0 + 18 \] Thus, we have: \[ p(x) + p(-x) = 18 \] ### Final Answer: \[ p(x) + p(-x) = 18 \]
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