Question

Which example correctly demonstrates polynomial addition?
A. (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10
B. (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -5x^2 + 3x + 8
C. (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = x^2 + 3x + 8
D. (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8

Answer 1

Which example correctly demonstrates polynomial subtraction?
A. (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10
B. (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -5x^2 + 3x + 8
C. (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = x^2 + 3x + 8
D. (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8

Answer 2

To correctly demonstrate polynomial addition, we need to add the like terms of the given polynomials. Let's look at the addition in choice C:

\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9)
\]

Now, we'll combine the like terms:

1. Combine the \(x^2\) terms: \(2x^2 + 3x^2 = 5x^2\)
2. Combine the \(x\) terms: \(6x + 3x = 9x\)
3. Combine the constant terms: \(1 + 9 = 10\)

Putting it all together, we get:

\[
5x^2 + 9x + 10
\]

Now we can compare this result with each option:

- **A.** \(5x^2 + 9x + 10\) (Correct, but this is a subtraction statement, not an addition).
- **B.** \(-5x^2 + 3x + 8\) (Incorrect).
- **C.** \(x^2 + 3x + 8\) (Incorrect).
- **D.** \(-x^2 + 3x - 8\) (Incorrect).

The correct demonstration of polynomial addition is NOT listed among the choices provided. However, the accurately computed addition is \(5x^2 + 9x + 10\) as shown from the correct calculation steps.

Thus, the answer based solely on polynomial addition should be \(5x^2 + 9x + 10\) but note that none of the choices were correct in demonstrating that operation directly.

Answer 3

To correctly demonstrate polynomial subtraction, we need to subtract the second polynomial from the first polynomial. Let's look at the subtraction in option A:

\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]

Now we'll distribute the negative sign and combine like terms:

1. Distributing the negative sign gives:
\[
(2x^2 + 6x + 1) - 3x^2 - 3x - 9
\]

2. Combine the \(x^2\) terms:
\[
2x^2 - 3x^2 = -1x^2 \text{ or } -x^2
\]

3. Combine the \(x\) terms:
\[
6x - 3x = 3x
\]

4. Combine the constant terms:
\[
1 - 9 = -8
\]

Putting it all together, we get:

\[
-x^2 + 3x - 8
\]

Now we can compare this result with the options provided:

- **A.** \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\) (Correct).
- **B.** \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -5x^2 + 3x + 8\) (Incorrect).
- **C.** \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = x^2 + 3x + 8\) (Incorrect).
- **D.** \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8\) (Incorrect).

Therefore, option **A** correctly demonstrates polynomial subtraction with the result \(-x^2 + 3x - 8\).