Add the polynomial expressions 2r^2−3r+4 and −2r^2+3r+6 .(1 point)

Answer 1

To add the polynomial expressions \( 2r^2 - 3r + 4 \) and \( -2r^2 + 3r + 6 \), you combine the like terms.

Here are the steps:

1. Write the expressions together: \[ (2r^2 - 3r + 4) + (-2r^2 + 3r + 6) \]

2. Combine the like terms:

   • For \( r^2 \) terms: \( 2r^2 + (-2r^2) = 0r^2 \) (which simplifies to \( 0 \))
   • For \( r \) terms: \( -3r + 3r = 0r \) (which simplifies to \( 0 \))
   • For the constant terms: \( 4 + 6 = 10 \)

3. Put it all together: \[ 0r^2 + 0r + 10 = 10 \]

So, the sum of the two polynomial expressions is \( 10 \).

Answer 2

Add the expressions. Expression 1: −3k+4k3−2 Expression 2: 9k2−3k3+4k−3 (2 points)

()k3+ ()k2+*)k+()

Answer 3

To add the polynomial expressions \( -3k + 4k^3 - 2 \) (Expression 1) and \( 9k^2 - 3k^3 + 4k - 3 \) (Expression 2), we will combine like terms.

Here are the steps:

1. Write the expressions together: \[ (4k^3 - 3k + 4 - 2) + (-3k^3 + 9k^2 + 4k - 3) \]

2. Combine the like terms:

   • For \( k^3 \) terms: \( 4k^3 + (-3k^3) = 1k^3 \)
   • For \( k^2 \) terms: There is no \( k^2 \) term in Expression 1, so we have \( 0k^2 + 9k^2 = 9k^2 \)
   • For \( k \) terms: \( -3k + 4k = 1k \)
   • For the constant terms: \( -2 + (-3) = -5 \)

3. Put it all together: \[ 1k^3 + 9k^2 + 1k - 5 \]

Now, filling in the blanks based on the format given:

• Coefficient for \( k^3 \): \( 1 \)
• Coefficient for \( k^2 \): \( 9 \)
• Coefficient for \( k \): \( 1 \)
• Constant term: \( -5 \)

So the result is: \[ (1)k^3 + (9)k^2 + (1)k + (-5) \]

Answer 4

Simplify (9x2−6x+2)−(x2+4x−39) .(1 point)

The difference of the polynomials is () .

Answer 5

To simplify the expression \( (9x^2 - 6x + 2) - (x^2 + 4x - 39) \), we will follow these steps:

1. Distribute the negative sign across the second polynomial: \[ 9x^2 - 6x + 2 - x^2 - 4x + 39 \]

2. Combine like terms:

   • \( x^2 \) terms: \( 9x^2 - x^2 = 8x^2 \)
   • \( x \) terms: \( -6x - 4x = -10x \)
   • Constant terms: \( 2 + 39 = 41 \)

3. Putting it all together gives us: \[ 8x^2 - 10x + 41 \]

So the difference of the polynomials is: \[ (8x^2 - 10x + 41) \]

Thus, the answer to fill in the blank is: \[ 8x^2 - 10x + 41 \]

Answer 6

Fill in the blanks to complete the polynomial equation that shows the subtraction of the second expression from the first and the resulting difference. (2 points)

9x^2 + ()x + 13 – 2x^2 + 12x +() ()x^2 + 5x + 2

Answer 7

To fill in the blanks in the polynomial equation that shows the subtraction of the second expression from the first and the resulting difference, we start with the expressions you provided:

1. First Expression: \( 9x^2 + bx + 13 \) (we need to find \( b \)).
2. Second Expression: \( - (2x^2 + 12x + c) \) (we need to find \( c \)).
3. Resulting Difference: \( dx^2 + 5x + 2 \) (we need to find \( d \) and confirm the coefficient for \( x \)).

Step 1: Write the subtraction equation

\[ (9x^2 + bx + 13) - (2x^2 + 12x + c) = dx^2 + 5x + 2 \]

Step 2: Perform the operation

First, distribute the negative sign: \[ 9x^2 + bx + 13 - 2x^2 - 12x - c = dx^2 + 5x + 2 \]

Step 3: Combine like terms

Combine the \( x^2 \), \( x \), and constant terms on the left side:

• \( x^2 \) terms: \( 9x^2 - 2x^2 = 7x^2 \)
• \( x \) terms: \( bx - 12x \)
• Constant terms: \( 13 - c \)

The equation now looks like: \[ (7x^2 + (b - 12)x + (13 - c)) = dx^2 + 5x + 2 \]

Step 4: Equate coefficients

Now we can set up equations based on the coefficients:

1. For \( x^2 \): \( 7 = d \)
2. For \( x \): \( b - 12 = 5 \)
3. For the constant: \( 13 - c = 2 \)

Step 5: Solve for \( b \) and \( c \)

• From \( b - 12 = 5 \): \[ b = 5 + 12 = 17 \]

• From \( 13 - c = 2 \): \[ c = 13 - 2 = 11 \]

Step 6: Fill in the blanks

Thus, the filled polynomial equation is: \[ 9x^2 + (17)x + 13 - (2x^2 + 12x + 11) = (7)x^2 + 5x + 2 \]

Final blanks filled:

• \( () = 17 \)
• \( () = 11 \)
• \( () = 7 \)

The complete equation is: \[ 9x^2 + \mathbf{17}x + 13 - (2x^2 + 12x + \mathbf{11}) = \mathbf{7}x^2 + 5x + 2 \]

Answer 8

Simplify (14x2−3x+2.25)+(0.75x2+2x−14) .(1 point)
The sum of the polynomials is ().

Answer 9

To simplify the expression \( (14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14) \), we'll combine the like terms.

Step 1: Write the expression together

\[ (14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14) \]

Step 2: Combine like terms

• For \( x^2 \) terms: \[ 14x^2 + 0.75x^2 = 14.75x^2 \]

• For \( x \) terms: \[ -3x + 2x = -1x \quad (\text{or simply } -x) \]

• For the constant terms: \[ 2.25 - 14 = -11.75 \]

Step 3: Write the result

Combining all these, the sum is: \[ 14.75x^2 - x - 11.75 \]

Thus, the sum of the polynomials is: \[ \boxed{14.75x^2 - x - 11.75} \]

Answer 10

Wrong answer it was x^2-x+2

Answer 11

Apologies for the confusion. Let's carefully add the polynomial expressions again step by step to see where the mistake might have occurred.

Given:

• First polynomial: \( 14x^2 - 3x + 2.25 \)
• Second polynomial: \( 0.75x^2 + 2x - 14 \)

Step 1: Align the expressions

\[ (14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14) \]

Step 2: Combine like terms

• For \( x^2 \) terms: \[ 14x^2 + 0.75x^2 = 14.75x^2 \]

• For \( x \) terms: \[ -3x + 2x = -1x \quad (\text{or simply } -x) \]

• For the constant terms: \[ 2.25 - 14 = -11.75 \]

Step 3: Combine all terms

Putting it all together, we have: \[ 14.75x^2 - x - 11.75 \]

Check against your result

You mentioned the sum was \( x^2 - x + 2 \). Let's analyze this equation:

If we factor \( 14.75x^2 - x - 11.75 \) to see if it could simplify to something closer to your result:

• The leading coefficient is quite different, and therefore, I believe my arithmetic regarding constants and coefficients didn't lead to that result.

Let's try it another way:

1. Convert values:

   • \( 2.25 = \frac{9}{4} \)
   • \( -14 \) remains \( -14 \)

2. Combine all together: Combine the equations directly using a common approach: \[ 14x^2 + 0.75x^2 = 14.75x^2 \quad \Rightarrow \quad \text{Not equal to the given } x^2 \] These are inconsistent. It seems I may have overlooked a clarity.

Recalculate:

Please clarify if the original terms should have been different. I will assist in ensuring the accuracy based on the original polynomials you provided. Thank you.