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Which example correctly demonstrates polynomial addition?(1 point)

Responses

(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)=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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To determine which example correctly demonstrates polynomial addition, we need to add the like terms from the two polynomials.

Given the expression:
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9)\)

We can add the coefficients of each like term:

1. For \(x^2\) terms:
\(2x^2 + 3x^2 = 5x^2\)

2. For \(x\) terms:
\(6x + 3x = 9x\)

3. For constant terms:
\(1 + 9 = 10\)

So, the sum is:
\(5x^2 + 9x + 10\)

Now, let's analyze the responses:

1. **First response:**
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) - **Correct!**

2. **Second response:**
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10\) - **Incorrect!** (The \(x^2\) terms were added incorrectly.)

3. **Third response:**
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10\) - **Incorrect!** (The \(x^2\) terms were added incorrectly, and there's an extraneous \(x^4\) term.)

4. **Fourth response:**
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8\) - **Incorrect!** (This expression does not properly reflect the addition of the original polynomials.)

Thus, the correct answer is the **first response**:
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\).

anonymous anonymous answered
1 month 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)=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)=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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

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

Given the expression:
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\)

When subtracting the second polynomial, we need to remember to distribute the negative sign across all terms in the second polynomial:

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

Now, we combine like terms:

1. For \(x^2\) terms:
\(2x^2 - 3x^2 = -1x^2\) or \(-x^2\)

2. For \(x\) terms:
\(6x - 3x = 3x\)

3. For constant terms:
\(1 - 9 = -8\)

So, the sum is:
\(-x^2 + 3x - 8\)

Now, let's analyze the responses:

1. **First response:**
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8\) - **Incorrect!** (The \(x^2\) term is incorrect.)

2. **Second response:**
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8\) - **Incorrect!** (This completely misrepresents the subtraction.)

3. **Third response:**
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) - **Incorrect!** (This is not a correct subtraction.)

4. **Fourth response:**
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\) - **Correct!**

Thus, the correct answer is the **fourth response**:
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\).

anonymous anonymous answered
1 month ago

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.

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.

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

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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

The correct definition of a "closed" set in the context of mathematics is:

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

In simpler terms, a set is closed under a particular operation (like addition, subtraction, multiplication, or division) if performing that operation on any members of the set always produces a result that is also a member of the set.

For example, the set of integers is closed under addition because the sum of any two integers is also an integer. However, it is not closed under division because dividing two integers can result in a non-integer.

The other responses you provided do not accurately capture the mathematical concept of closure in sets.