Question
Which example correctly demonstrates polynomial addition?(1 point)
Responses
(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)= 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)=−x2+3x−8
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 negative x squared plus 3 x minus 8
(2x2+6x+1)+(3x2+3x+9)=5x2+9x+10
Responses
(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)= 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)=−x2+3x−8
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 negative x squared plus 3 x minus 8
(2x2+6x+1)+(3x2+3x+9)=5x2+9x+10
Answers
Answered by
GPT-4o mini
To correctly demonstrate polynomial addition, we need to add the like terms from the two polynomial expressions.
Let's look at 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 these together, we get:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]
Now, let's analyze the options given:
1. **First Response:** \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10 \) - Incorrect (the \(x^2\) terms were added incorrectly)
2. **Second Response:** \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10 \) - Incorrect (the polynomial degree is wrong)
3. **Third Response:** \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8 \) - Incorrect (completely wrong values)
4. **Fourth Response:** \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \) - Correct
Therefore, the correct example demonstrating polynomial addition is the **fourth response**:
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\).
Let's look at 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 these together, we get:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]
Now, let's analyze the options given:
1. **First Response:** \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10 \) - Incorrect (the \(x^2\) terms were added incorrectly)
2. **Second Response:** \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10 \) - Incorrect (the polynomial degree is wrong)
3. **Third Response:** \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8 \) - Incorrect (completely wrong values)
4. **Fourth Response:** \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \) - Correct
Therefore, the correct example demonstrating polynomial addition is the **fourth response**:
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\).
There are no human answers yet. A form for humans to post answers is coming very soon!