Question
Question
Which example correctly demonstrates polynomial addition?(1 point)
Responses
(2x2+6x+1)+(3x2+3x+9)= 5x4+9x2+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 3 x squared right parenthesis plus left parenthesis 6 x plus 3 x right parenthesis plus left parenthesis 1 plus 9 right parenthesis
(2x2+6x+1)+(3x2+3x+9)=13x2+9x+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 3 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 6 x plus 9 right parenthesis
(2x2+6x+1)+(3x2+3x+9)=5x2+9x+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus 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
Which example correctly demonstrates polynomial addition?(1 point)
Responses
(2x2+6x+1)+(3x2+3x+9)= 5x4+9x2+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 3 x squared right parenthesis plus left parenthesis 6 x plus 3 x right parenthesis plus left parenthesis 1 plus 9 right parenthesis
(2x2+6x+1)+(3x2+3x+9)=13x2+9x+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 3 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 6 x plus 9 right parenthesis
(2x2+6x+1)+(3x2+3x+9)=5x2+9x+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus 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
Answers
GPT-4o mini
To demonstrate polynomial addition correctly, we need to combine like terms from the two polynomials given.
Starting with the expression:
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9)\)
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:
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\)
Now, let's look at the responses given:
1. **First Response:** Incorrect. It results in \(5x^4 + 9x^2 + 10\).
2. **Second Response:** Incorrect. It claims \(13x^2 + 9x + 10\), which adds the \(x^2\) terms incorrectly.
3. **Third Response:** Correct. Displays \(5x^2 + 9x + 10\).
4. **Fourth Response:** Incorrect. Claims \(-x^2 + 3x - 8\).
Therefore, the correct example that demonstrates polynomial addition is:
**(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10**
Starting with the expression:
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9)\)
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:
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\)
Now, let's look at the responses given:
1. **First Response:** Incorrect. It results in \(5x^4 + 9x^2 + 10\).
2. **Second Response:** Incorrect. It claims \(13x^2 + 9x + 10\), which adds the \(x^2\) terms incorrectly.
3. **Third Response:** Correct. Displays \(5x^2 + 9x + 10\).
4. **Fourth Response:** Incorrect. Claims \(-x^2 + 3x - 8\).
Therefore, the correct example that demonstrates polynomial addition is:
**(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10**