Fill in the missing values to show that polynomials form a closed system under subtraction.

Question

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

Answer 1

To show that polynomials form a closed system under subtraction, we need to subtract the two given polynomials and determine the missing values.

First, let's subtract the x^2 terms: 9x^2 - 2x^2 = 7x^2
Next, let's subtract the x terms: x - 12x = -11x
Finally, let's subtract the constant terms: 13 - 2 = 11

So, the missing values are:
-11x (for the missing x term)
7x^2 (for the missing x^2 term)
11 (for the missing constant term)

Putting it all together, the subtracted polynomial is:
7x^2 - 11x + 11