To demonstrate polynomial addition, let's take two polynomial examples and show how to add them.
Let: \[ P(x) = 3x^3 + 2x^2 + 5 \] \[ Q(x) = 4x^3 + x + 7 \]
To add these two polynomials, we combine like terms:
- First, organize the polynomials by their degree:
- For \( x^3 \): \( 3x^3 + 4x^3 = 7x^3 \)
- For \( x^2 \): \( 2x^2 \) (there is no corresponding term in \( Q(x) \))
- For \( x^1 \): \( 0 + x = x \) (the coefficient of \( x \) in \( P(x) \) is 0)
- For the constant term: \( 5 + 7 = 12 \)
Putting this together, we have: \[ P(x) + Q(x) = 7x^3 + 2x^2 + x + 12 \]
Thus, the sum of the two polynomials \( P(x) \) and \( Q(x) \) is: \[ 7x^3 + 2x^2 + x + 12 \]
This is a correct demonstration of polynomial addition.
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