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)

Question

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

x2
+ 5x
+ 2

Answer 1

To complete the polynomial subtraction equation, we need to subtract the second expression from the first expression. Here is how it looks:

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

2. The second expression is:
   \( 2x^2 + 12x + (x^2 + 5x + 2) \)

Now, let's simplify the second expression before proceeding with the subtraction:

• Combine the terms in the second expression: \[ 2x^2 + 12x + x^2 + 5x + 2 = (2x^2 + x^2) + (12x + 5x) + 2 = 3x^2 + 17x + 2 \]

Now we can write the polynomial subtraction equation:

• So, we need to subtract: \[ 9x^2 + x + 13 - (3x^2 + 17x + 2) = (9x^2 - 3x^2) + (x - 17x) + (13 - 2) \]

Now we simplify that: \[ (9 - 3)x^2 + (1 - 17)x + (13 - 2) = 6x^2 - 16x + 11 \]

Putting it all together, the filled equation is: \[ 9x^2 + x + 13 - (2x^2 + 12x + (x^2 + 5x + 2)) = 6x^2 - 16x + 11 \]

Thus, the complete equation with the blanks filled is: \[ 9x^2 + x + 13 - (2x^2 + 12x + 2) = 6x^2 - 16x + 11 \]