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If P(x) =x+3, then p(x)+p(-x) is equal...

If `P(x) =x+3,` then `p(x)+p(-x) ` is equal to

A

3

B

2`x`

C

zero

D

6

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the value of \( P(x) + P(-x) \) given that \( P(x) = x + 3 \). ### Step-by-Step Solution: 1. **Given Polynomial:** \[ P(x) = x + 3 \] 2. **Find \( P(-x) \):** Substitute \( -x \) into the polynomial \( P(x) \): \[ P(-x) = -x + 3 \] 3. **Add \( P(x) \) and \( P(-x) \):** \[ P(x) + P(-x) = (x + 3) + (-x + 3) \] 4. **Combine Like Terms:** \[ P(x) + P(-x) = x + 3 - x + 3 \] 5. **Simplify the Expression:** \[ P(x) + P(-x) = (x - x) + (3 + 3) \] \[ P(x) + P(-x) = 0 + 6 \] \[ P(x) + P(-x) = 6 \] So, the value of \( P(x) + P(-x) \) is \( 6 \).
To solve the problem, we need to find the value of \( P(x) + P(-x) \) given that \( P(x) = x + 3 \). ### Step-by-Step Solution: 1. **Given Polynomial:** \[ P(x) = x + 3 \] ...
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