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

Answer 1

To complete the polynomial equation that shows the subtraction of the second expression from the first, we will set up the equation based on the information given and perform the subtraction.

Let's denote the first polynomial as \( A \) and the second as \( B \):

1. \( A = 9x^2 + x + 13 \)
2. \( B = 2x^2 + 12x + (x^2 + 5x + 2) \)

Now we can combine the terms in \( B \):
\[
B = 2x^2 + 12x + x^2 + 5x + 2 = (2x^2 + x^2) + (12x + 5x) + 2 = 3x^2 + 17x + 2
\]

Now we need to perform the subtraction \( A - B \):
\[
A - B = (9x^2 + x + 13) - (3x^2 + 17x + 2)
\]

Now, we distribute the negative sign to each term in \( B \):
\[
A - B = 9x^2 + x + 13 - 3x^2 - 17x - 2
\]

Now, we can combine like terms:
- For \( x^2 \) terms: \( 9x^2 - 3x^2 = 6x^2 \)
- For \( x \) terms: \( x - 17x = -16x \)
- For constant terms: \( 13 - 2 = 11 \)

Thus, we find:
\[
A - B = 6x^2 - 16x + 11
\]

So, the completed polynomial equation is:
\[
9x^2 + x + 13 - (2x^2 + 12x + (x^2 + 5x + 2)) = 6x^2 - 16x + 11
\]

So, your filled-in blanks would look like:
- **First Polynomial**: \( 9x^2 + x + 13 \)
- **Second Polynomial**: \( 3x^2 + 17x + 2 \) (the simplified form after combining, which includes \( 2x^2 + 12x + x^2 + 5x + 2 \))
- **Resulting Difference**: \( 6x^2 - 16x + 11 \)