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)

Question

9x^2
+
x + 13
– 2x^2
+ 12x
+

x^2
+ 5x
+ 2

Answer 1

To complete the polynomial equation, we will subtract the second expression from the first and determine the resulting difference.

Given the first expression: \( 9x^2 + x + 13 \)

And the second expression: \( 2x^2 + 12x + (x^2 + 5x + 2) \)

First, we need to combine the terms of the second expression:

• Combine the \( x^2 \) terms:

  • \( 2x^2 + x^2 = 3x^2 \)

• Combine the \( x \) terms:

  • \( 12x + 5x = 17x \)

• The constant term remains \( 2 \).

Thus, the second expression simplifies to: \( 3x^2 + 17x + 2 \)

Now, we can perform the subtraction: \[ (9x^2 + x + 13) - (3x^2 + 17x + 2) \]

Distributing the negative sign across the terms of the second expression: \[ 9x^2 + x + 13 - 3x^2 - 17x - 2 \]

Now, combine like terms.

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

   • \( 9x^2 - 3x^2 = 6x^2 \)

2. For \( x \) terms:

   • \( x - 17x = -16x \)

3. For constant terms:

   • \( 13 - 2 = 11 \)

Therefore, the resulting expression after subtracting is: \[ 6x^2 - 16x + 11 \]

Now we can fill in the blanks:

• The term representing the missing expression after subtraction is \( 3x^2 + 17x + 2 \).
• The resulting difference is \( 6x^2 - 16x + 11 \).

So the completed polynomial equation is: \[ 9x^2 + x + 13 - (3x^2 + 17x + 2) = 6x^2 - 16x + 11 \]

Answer 2

bot are you sure?

Answer 3

Let’s go through the problem step by step again to ensure accuracy.

1. First Expression: \[ 9x^2 + x + 13 \]

2. Second Expression: \[ 2x^2 + 12x + (x^2 + 5x + 2) \]

   We need to simplify the second expression first:

   • Combine \( x^2 \) terms: \[ 2x^2 + x^2 = 3x^2 \]
   • Combine \( x \) terms: \[ 12x + 5x = 17x \]
   • The constant term remains \( 2 \).

   Therefore, the second expression simplifies to: \[ 3x^2 + 17x + 2 \]

3. Now we perform the subtraction: \[ (9x^2 + x + 13) - (3x^2 + 17x + 2) \]

   When we distribute the negative sign: \[ 9x^2 + x + 13 - 3x^2 - 17x - 2 \]

4. Combining like terms:

   • For \( x^2 \) terms: \[ 9x^2 - 3x^2 = 6x^2 \]
   • For \( x \) terms: \[ x - 17x = -16x \]
   • For constants: \[ 13 - 2 = 11 \]

Therefore, the final result after performing the subtraction is: \[ 6x^2 - 16x + 11 \]

So the filled in polynomial equation is: \[ 9x^2 + x + 13 - (3x^2 + 17x + 2) = 6x^2 - 16x + 11 \]

This result appears to be accurate based on the calculations provided. If there's anything specific you'd like to clarify or if I misunderstood your question, please let me know!

Answer 4

bot each equation needs to be separate from each other

Answer 5

I understand now that you want the equations separated clearly to show the subtraction process step by step. Let’s format it properly.

1. First Expression: \[ 9x^2 + x + 13 \]

2. Second Expression: \[ 2x^2 + 12x + (x^2 + 5x + 2) \]

   Simplifying the second expression:

   • Combine \( x^2 \) terms: \[ 2x^2 + x^2 = 3x^2 \]
   • Combine \( x \) terms: \[ 12x + 5x = 17x \]
   • The constant term remains: \[
     • 2 \]

   So the second expression becomes: \[ 3x^2 + 17x + 2 \]

3. Subtraction Setup: We want to subtract the second expression from the first: \[ (9x^2 + x + 13) - (3x^2 + 17x + 2) \]

4. Distributing the Negative Sign: \[ 9x^2 + x + 13 - 3x^2 - 17x - 2 \]

5. Combine Like Terms:

   • For \( x^2 \) terms: \[ 9x^2 - 3x^2 = 6x^2 \]
   • For \( x \) terms: \[ x - 17x = -16x \]
   • For the constant terms: \[ 13 - 2 = 11 \]

6. Final Result: Thus, the result of the subtraction is: \[ 6x^2 - 16x + 11 \]

Finally, putting it all together, the filled-in polynomial equation, clearly separated, looks like this:

\[ 9x^2 + x + 13 \] \[

• (3x^2 + 17x + 2) \] \[ = 6x^2 - 16x + 11 \]

If this format is what you were looking for, let me know! Thank you for your patience.