Question

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)
  9x2
+ x + 13
– 2x2
+ 12x
+
  x2
+ 5x
+ 2

Answer 1

To fill in the blanks for the polynomial equation that shows the subtraction of the second expression from the first, we can proceed step-by-step with the given expressions.

The first expression is:
\( 9x^2 + x + 13 \)

The second expression to subtract is:
\( 2x^2 + 12x + \_\_ \)

The third expression is:
\( x^2 + 5x + 2 \)

We need to subtract the second and third expressions from the first expression:
1. Combine the second and third expressions for subtraction. Let's first evaluate:

\[
2x^2 + 12x + (x^2 + 5x + 2) = 2x^2 + 12x + x^2 + 5x + 2 = (2x^2 + x^2) + (12x + 5x) + 2
\]

This results in:
\[
3x^2 + 17x + 2
\]

2. Now we perform the subtraction from the first expression:

\[
9x^2 + x + 13 - (3x^2 + 17x + 2)
\]

Distributing the negative sign, we have:
\[
9x^2 + x + 13 - 3x^2 - 17x - 2
\]

3. Now combine like terms:

- For \(x^2\): \(9x^2 - 3x^2 = 6x^2\)
- For \(x\): \(x - 17x = -16x\)
- For the constant term: \(13 - 2 = 11\)

The resulting difference is:
\[
6x^2 - 16x + 11
\]

4. So, the blanks can be filled with:
- The second expression gives us a missing constant term: \(2\)
- The resulting polynomial from the subtraction is: \(6x^2 - 16x + 11\)

Thus, putting it all together, the complete polynomial equation can be represented as:

\[
9x^2 + x + 13 - (2x^2 + 12x + 2) = 6x^2 - 16x + 11
\]

**Completion of the statement**:
- The blank for the second expression is **2**, and based on the subtraction and combination, the resulting difference is **6x² - 16x + 11**.