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)
9x^2 + ___x + 13
- 2x^2 + 12x + ___
___x^2 + 5x + 2

Answer 1

To complete the polynomial equation, we need to subtract the second polynomial from the first and find the missing values. The equation starts as follows:

\[
9x^2 + ___x + 13
- 2x^2 + 12x + ___
\]

Now, let's perform the subtraction step by step.

1. **Subtract the coefficients of \(x^2\)**:
\[
9x^2 - 2x^2 = 7x^2
\]

2. **Subtract the coefficients of \(x\)**:
We want to find the coefficient of \(x\) in the first polynomial to subtract 12 from it. Let’s denote it as \(a\):
\[
a - 12 = 5
\]
Solving for \(a\):
\[
a = 5 + 12 = 17
\]

3. **Subtract the constant terms**:
We need to find the missing constant in the second polynomial. Let’s denote it as \(b\):
\[
13 - b = 2
\]
Solving for \(b\):
\[
b = 13 - 2 = 11
\]

Now we have all of the values:

- The coefficient of \(x\) in the first polynomial is \(17\).
- The missing constant from the second polynomial is \(11\).

Bringing it all together, we can fill in the blanks:

\[
9x^2 + 17x + 13
- 2x^2 + 12x + 11
= 7x^2 + 5x + 2
\]

So, the completed equation is:

\[
\begin{aligned}
&9x^2 + 17x + 13 \\
&- 2x^2 + 12x + 11 \\
&= 7x^2 + 5x + 2
\end{aligned}
\]

Final Answer:
**17** for the first blank (coefficient of \(x\)), **11** for the second blank (constant in the second polynomial).