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)
Complete the polynomial subtraction equation.
9x2
+
x + 13
– 2x2
+ 12x
+

x2
+ 5x
+ 2

Answer 1

To complete the polynomial subtraction equation, we first need to correctly set up the expression as follows:

Starting with the first polynomial:
\[ 9x^2 + x + 13 \]

Subtracting the second polynomial:
\[ 2x^2 + 12x + (x^2 + 5x + 2) \]

Let's rewrite the second polynomial in total:
- Combine the terms: \( 2x^2 + x^2 + 12x + 5x + 2 \), which simplifies to \( 3x^2 + 17x + 2 \).

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

Combine the terms:
1. For \( x^2 \): \( 9x^2 - 3x^2 = 6x^2 \)
2. For \( x \): \( x - 17x = -16x \)
3. For the constant: \( 13 - 2 = 11 \)

This results in:
\[ 6x^2 - 16x + 11 \]

Thus, to fill in the blanks, we have:
1. The first blank for the second polynomial is \( 2x^2 \).
2. The second blank is \( 12x \).
3. The third blank is \( 2 \).

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