Question

Question

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

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

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

−5p2−4p+7

Answer 1

To add the polynomial expressions \( 3 - 2p - 5p^2 \) and \( p^4 - 3p + 4 \), we can first rewrite them aligned by their degrees:

\[ 3 - 2p - 5p^2 + (p^4 - 3p + 4) \]

Now, group the like terms:

• The \( p^4 \) term: \( p^4 \)
• The \( p^2 \) term: \( -5p^2 \)
• The \( p \) terms: \( -2p - 3p = -5p \)
• The constant terms: \( 3 + 4 = 7 \)

Now, combining these, we get:

\[ p^4 - 5p^2 - 5p + 7 \]

Thus, the final result of adding the two polynomial expressions is:

\[ p^4 - 5p^2 - 5p + 7 \]

So the correct response is:

p^4 - 5p^2 - 5p + 7

Answer 2

What is (3x2−2)+(11−5x)?(1 point)
Responses

2x2−9
2 x squared minus 9

3x2−5x+9
3 x squared minus 5 x plus 9

−2x2+9
negative 2 x squared plus 9

3x2+5x−9

Answer 3

To add the expressions \( (3x^2 - 2) + (11 - 5x) \), we can simply combine like terms.

Start by rewriting the expression with the terms aligned:

\[ 3x^2 - 2 + 11 - 5x \]

Now, we can combine the constant terms \( -2 \) and \( 11 \):

\[ 3x^2 - 5x + (11 - 2) \] \[ 3x^2 - 5x + 9 \]

Thus, the resulting polynomial is:

\[ 3x^2 - 5x + 9 \]

The correct response is:

3x^2 - 5x + 9

Answer 4

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

(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
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

Answer 5

To determine which example correctly demonstrates polynomial addition, let's add the two polynomials \( (2x^2 + 6x + 1) \) and \( (3x^2 + 3x + 9) \) step by step.

Starting with:

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

Combine the like terms:

1. Combine \(x^2\) terms:

   • \(2x^2 + 3x^2 = 5x^2\)

2. Combine \(x\) terms:

   • \(6x + 3x = 9x\)

3. Combine constant terms:

   • \(1 + 9 = 10\)

Now put it all together:

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

Now let’s compare this result with the responses given:

1. (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8 - Incorrect

2. (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10 - Incorrect

3. (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10 - Incorrect

4. (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 - Correct

Therefore, the correct answer is:

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

Answer 6

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

(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)=−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 left parenthesis 2 x squared plus 6 x minus 4 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 4 right parenthesis

(2x2+6x+1)−(3x2+3x+9)=−x2+3x−8

Answer 7

To determine which example correctly demonstrates polynomial subtraction, let's perform the subtraction of the polynomials \( (2x^2 + 6x + 1) \) and \( (3x^2 + 3x + 9) \).

Start with:

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

Distributing the negative sign to the second polynomial:

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

Now, combine the like terms:

1. Combine \(x^2\) terms:

   • \(2x^2 - 3x^2 = -x^2\)

2. Combine \(x\) terms:

   • \(6x - 3x = 3x\)

3. Combine constant terms:

   • \(1 - 9 = -8\)

Putting it all together, we get:

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

Now let's compare this result with the responses given:

1. (2x² + 6x + 1) - (3x² + 3x + 9) = 5x² + 9x + 10 - Incorrect

2. (2x² + 6x + 1) - (3x² + 3x + 9) = -5x² + 3x - 8 - Incorrect

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

4. (2x² + 6x + 1) - (3x² + 3x + 9) = -x² + 3x - 8 - Correct

Therefore, the correct answer is:

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

Answer 8

What does it mean for a set to be "closed"?(1 point)
Responses

An expression belonging to a closed set cannot be used to create an expression that is not of that set.
An expression belonging to a closed set cannot be used to create an expression that is not of that set.

Members of a closed set cannot be added, subtracted, multiplied, or divided.
Members of a closed set cannot be added, subtracted, multiplied, or divided.

The set has a finite number of members, as opposed to being infinitely large.
The set has a finite number of members, as opposed to being infinitely large.

An operation performed on members of that set will result in a member of the same set.

Answer 9

The term "closed" in the context of sets, particularly in mathematics, refers to the property of a set under a specific operation. A set is said to be closed under an operation (such as addition, subtraction, multiplication, etc.) if performing that operation on any members of the set results in a value that is also a member of that set.

Therefore, the correct response is:

An operation performed on members of that set will result in a member of the same set.