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Add the polynomial expressions 3−2p−5p2 and p4−3p+4 .(1 point)

Responses

−5p2−4p+7
negative 5 p squared minus 4 p plus 7

p4−5p2−5p+7
p superscript 4 baseline minus 5 p squared minus 5 p plus 7

p4−5p2−6p+7
p superscript 4 baseline minus 5 p squared minus 6 p plus 7

−4p2−5p+7
negative 4 p squared minus 5 p plus 7

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

To add the polynomial expressions \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we will combine like terms:

1. Start with the two polynomials:
- \(3 - 2p - 5p^2\)
- \(p^4 - 3p + 4\)

2. Arrange the terms by their degrees:
- \(p^4 + 0p^3 - 5p^2 + (-2p - 3p) + (3 + 4)\)

3. Perform the addition for each type of term:
- For \(p^4\): \(1\)
- For \(p^3\): \(0\)
- For \(p^2\): \(-5\)
- For \(p\): \(-2 - 3 = -5\)
- For the constant: \(3 + 4 = 7\)

Putting it all together, we get:
\[
p^4 - 5p^2 - 5p + 7
\]

The correct response is:
**\(p^4 - 5p^2 - 5p + 7\)** (or in the second response format: \(p \text{ superscript } 4 \text{ baseline } - 5 p^2 - 5 p + 7\)).

anonymous anonymous answered
2 months ago

What is (3x2−2)+(11−5x)?(1 point)

Responses

3x2−5x+9
3 x squared minus 5 x plus 9

2x2−9
2 x squared minus 9

3x2+5x−9
3 x squared plus 5 x minus 9

−2x2+9

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

To simplify the expression \((3x^2 - 2) + (11 - 5x)\), we will combine like terms:

1. Start with the two polynomials:
- \(3x^2 - 2\)
- \(11 - 5x\)

2. Rearrange the terms:
- Combine \(3x^2\), \(-5x\), and the constants \(-2\) and \(11\).

3. Perform the addition for each type of term:
- The \(x^2\) term: \(3x^2\)
- The \(x\) term: \(-5x\)
- The constant terms: \(-2 + 11 = 9\)

Putting it all together, we get:
\[
3x^2 - 5x + 9
\]

The correct response is:
**\(3x^2 - 5x + 9\)** (or in the response format: \(3 x \text{ squared } - 5 x + 9\)).

anonymous anonymous answered
2 months ago

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)=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
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)= 5x4+9x2+10

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

To determine which example correctly demonstrates polynomial addition, let's perform the addition of the two polynomials:

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

Now, we'll combine 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 have:

\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]

Now we can analyze the options:

1. **Option 1** states:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10 \quad \text{(Incorrect)}
\]

2. **Option 2** states:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \quad \text{(Correct)}
\]

3. **Option 3** states:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8 \quad \text{(Incorrect)}
\]

4. **Option 4** states:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10 \quad \text{(Incorrect)}
\]

The correct demonstration of polynomial addition is:

**(2x² + 6x + 1) + (3x² + 3x + 9) = 5x² + 9x + 10** (Option 2).

anonymous anonymous answered
2 months ago

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)=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
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)=x2+3x+8

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

To determine which example correctly demonstrates polynomial subtraction, let's perform the subtraction of the two polynomials:

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

We can distribute the negative sign across the second polynomial:

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

Now, we will combine like terms:

1. **Combine the \(x^2\) terms:**
\(-3x^2 + 2x^2 = -1x^2\) or \(-x^2\)

2. **Combine the \(x\) terms:**
\(6x - 3x = 3x\)

3. **Combine the constant terms:**
\(1 - 9 = -8\)

Putting it all together, we have:

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

Now we can analyze the options:

1. **Option 1** states:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8 \quad \text{(Incorrect)}
\]

2. **Option 2** states:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \quad \text{(Incorrect)}
\]

3. **Option 3** states:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8 \quad \text{(Correct)}
\]

4. **Option 4** states:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8 \quad \text{(Incorrect)}
\]

The correct demonstration of polynomial subtraction is:

**(2x² + 6x + 1) - (3x² + 3x + 9) = -x² + 3x - 8** (Option 3).