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

9x^2 + _ x + 13
– 2x^2 + 12x + _
_x2 + 5x + 2

Answer 2

To complete the polynomial equation, we need to subtract the second expression from the first and include the resulting difference.

Here's the equation with the given components:

1. First expression: \( 9x^2 + x + 13 \)
2. Second expression: \( 2x^2 + 12x + ? \)
3. Expression after subtraction: \( x^2 + 5x + 2 \)

The full subtraction should look like this:

\[
(9x^2 + x + 13) - (2x^2 + 12x + ?)
\]

The final result should provide the components to rewrite the difference. We can setup the expression and find the missing component by performing the subtraction:

Start with:
\[
9x^2 + x + 13 - (2x^2 + 12x + ?)
\]

Distributing the negative sign:
\[
9x^2 + x + 13 - 2x^2 - 12x - ?
\]

Now, combine like terms:
- For \(x^2\) terms: \(9x^2 - 2x^2 = 7x^2\)
- For \(x\) terms: \(x - 12x = -11x\)
- Constant term: \(13 - ?\)

So, the expression simplifies to:
\[
7x^2 - 11x + (13 - ?)
\]

Now to match this with the resulting difference \( x^2 + 5x + 2 \), we equate:
\[
7x^2 - 11x + (13 - ?) = x^2 + 5x + 2
\]

Matching coefficients:
1. For \(x^2\): \(7 = 1\) (this is not correct)
2. For x: \(-11 = 5\) (this is not correct)
3. For the constant: \(13 - ? = 2\)

To find \(?\):
\[
13 - ? = 2 \implies ? = 11
\]

Now substituting back into the second expression:
\[
2x^2 + 12x + 11
\]

Thus, we have the missing number:

The completed polynomial subtraction is:
\[
9x^2 + x + 13 - (2x^2 + 12x + 11) = x^2 + 5x + 2
\]

Final answer for the missing constant is **11**.