Question

Which example correctly demonstrates polynomial subtraction?(1 point)
Responses

(2x2+6x+1)−(3x2+3x+9)=−5x2+3x−8
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals 2 x squared plus 6 x plus 1 minus 3 x squared minus 3 x minus 9

(2x2+6x+1)−(3x2+3x+9)=−x2+3x−8
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals negative x squared plus 3 x minus 8

(2x2+6x+1)−(3x2+3x+9)=5x2+9x+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals 5 x squared plus 9 x plus 10

(2x2+6x+1)−(3x2+3x+9)=x2+3x+8

Answer 1

To determine which example correctly demonstrates polynomial subtraction, we will perform the subtraction of the two polynomials: \( (2x^2 + 6x + 1) - (3x^2 + 3x + 9) \).

First, we can rewrite the subtraction as follows:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

Next, we combine the like terms:

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

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

3. For the constant terms:
\[
1 - 9 = -8
\]

Putting this all together, we have:
\[
-x^2 + 3x - 8
\]

Now, let's compare this with the responses:

1. **Response 1**: \(-5x^2 + 3x - 8\) (Incorrect)
2. **Response 2**: \(-x^2 + 3x - 8\) (Correct)
3. **Response 3**: \(5x^2 + 9x + 10\) (Incorrect)
4. **Response 4**: \(x^2 + 3x + 8\) (Incorrect)

Therefore, the correct example that demonstrates polynomial subtraction is:

\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]

Thus, **Response 2** is the correct answer.