Add the polynomial expressions 3−2p−5p2 and p4−3p+4 .(1 point)%0D%0AResponses%0D%0A%0D%0A−5p2−4p+7%0D%0Anegative 5 p squared minus 4 p plus 7%0D%0A%0D%0Ap4−5p2−5p+7%0D%0Ap superscript 4 baseline minus 5 p squared minus 5 p plus 7%0D%0A%0D%0Ap4−5p2−6p+7%0D%0Ap superscript 4 baseline minus 5 p squared minus 6 p plus 7%0D%0A%0D%0A−4p2−5p+7%0D%0Anegative 4 p squared minus 5 p plus 7

Answer 1

To add the polynomials \(3 - 2p - 5p^2\) and \(p^4 - 3p + 4\), we combine like terms.

1. Write down the expressions: \[ 3 - 2p - 5p^2 \] and \[ p^4 - 3p + 4 \]

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

3. Combine the like terms:

   • For \(p^4\): \(p^4\)
   • For \(p^3\): \(0\) (there's no \(p^3\) term)
   • For \(p^2\): \(-5p^2\)
   • For \(p\): \(-2p - 3p = -5p\)
   • For the constant: \(3 + 4 = 7\)

Putting it all together, the result is: \[ p^4 - 5p^2 - 5p + 7 \]

Thus, the correct answer is: \[ \boxed{p^4 - 5p^2 - 5p + 7} \]

Answer 2

What is (3x2−2)+(11−5x) ?(1 point) Responses 2x2−9 2 x squared minus 9 −2x2+9 negative 2 x squared plus 9 3x2+5x−9 3 x squared plus 5 x minus 9 3x2−5x+9

Answer 3

To simplify the expression \((3x^2 - 2) + (11 - 5x)\), follow these steps:

1. Distribute and organize the terms: \[ 3x^2 - 2 + 11 - 5x \]

2. Combine like terms:

   • The \(x^2\) term: \(3x^2\)
   • The \(x\) term: \(-5x\) (there's no other \(x\) term to combine with)
   • The constant terms: \(-2 + 11 = 9\)

3. Put it all together: \[ 3x^2 - 5x + 9 \]

Thus, the simplified expression is: \[ \boxed{3x^2 - 5x + 9} \]

Answer 4

Which example correctly demonstrates polynomial addition?(1 point)%0D%0AResponses%0D%0A%0D%0A(2x2+6x+1)+(3x2+3x+9)=−x2+3x−8%0D%0Aleft 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%0D%0A%0D%0A(2x2+6x+1)+(3x2+3x+9)=5x2+9x+10%0D%0Aleft 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%0D%0A%0D%0A(2x2+6x+1)+(3x2+3x+9)=13x2+9x+10%0D%0Aleft 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%0D%0A%0D%0A(2x2+6x+1)+(3x2+3x+9)= 5x4+9x2+10

Answer 5

To determine which example correctly demonstrates polynomial addition, we'll first perform the addition of the two polynomials: \[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) \]

1. Combine like terms:

   • The \(x^2\) terms: \(2x^2 + 3x^2 = 5x^2\)
   • The \(x\) terms: \(6x + 3x = 9x\)
   • The constant terms: \(1 + 9 = 10\)

2. Putting it all together, we get: \[ 5x^2 + 9x + 10 \]

Now, let's examine the responses to find the correct demonstration:

1. \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8\) (Incorrect)
2. \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) (Correct)
3. \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10\) (Incorrect)
4. \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10\) (Incorrect)

The correct example that demonstrates polynomial addition is: \[ \boxed{(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10} \]

Answer 6

Which example correctly demonstrates polynomial subtraction?(1 point)%0D%0AResponses%0D%0A%0D%0A(2x2+6x+1)−(3x2+3x+9)=−5x2+3x−8%0D%0Aleft 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%0D%0A%0D%0A(2x2+6x+1)−(3x2+3x+9)=x2+3x+8%0D%0Aleft 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%0D%0A%0D%0A(2x2+6x+1)−(3x2+3x+9)=5x2+9x+10%0D%0Aleft 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%0D%0A%0D%0A(2x2+6x+1)−(3x2+3x+9)=−x2+3x−8%0D%0Aleft 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

Answer 7

To determine which example correctly demonstrates polynomial subtraction, we will perform the subtraction of the two polynomials:

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

1. Rewrite the expression, distributing the negative sign: \[ 2x^2 + 6x + 1 - 3x^2 - 3x - 9 \]

2. Combine like terms:

   • The \(x^2\) terms: \(2x^2 - 3x^2 = -x^2\)
   • The \(x\) terms: \(6x - 3x = 3x\)
   • The constant terms: \(1 - 9 = -8\)

3. Putting it all together, we get: \[ -x^2 + 3x - 8 \]

Now, let's examine the given responses to find the correct demonstration:

1. Response 1: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8\) (Incorrect)
2. Response 2: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8\) (Incorrect)
3. Response 3: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) (Incorrect)
4. Response 4: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\) (Correct)

Thus, the correct example that demonstrates polynomial subtraction is: \[ \boxed{(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8} \]

Answer 8

What does it mean for a set to be "closed"?(1 point)%0D%0AResponses%0D%0A%0D%0AAn expression belonging to a closed set cannot be used to create an expression that is not of that set.%0D%0AAn expression belonging to a closed set cannot be used to create an expression that is not of that set.%0D%0A%0D%0AAn operation performed on members of that set will result in a member of the same set.%0D%0AAn operation performed on members of that set will result in a member of the same set.%0D%0A%0D%0AMembers of a closed set cannot be added, subtracted, multiplied, or divided.%0D%0AMembers of a closed set cannot be added, subtracted, multiplied, or divided.%0D%0A%0D%0AThe set has a finite number of members, as opposed to being infinitely large.

Answer 9

In mathematics, a set is said to be "closed" under a particular operation if performing that operation on members of the set always produces a member of the same set.

For instance, if you take two numbers from a set and add them together, and the result is still a number in that set, then the set is closed under addition.

Given your response options, the correct statement regarding closure is:

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

So the best answer is: \[ \boxed{\text{An operation performed on members of that set will result in a member of the same set.}} \]