Which example correctly demonstrates polynomial subtraction?

Question

A) (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8
B) (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8
C) 2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10
D) 2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8

Answer 1

To solve the polynomial subtraction (2x^2 + 6x + 1) - (3x^2 + 3x + 9), we first need to distribute the negative sign across the second polynomial.

So, we start with:

(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 2x^2 + 6x + 1 - 3x^2 - 3x - 9

Now, we combine like terms:

1. Combine the \( x^2 \) terms: \( 2x^2 - 3x^2 = -1x^2 \) or \(-x^2\)

2. Combine the \( x \) terms: \( 6x - 3x = 3x \)

3. Combine the constant terms: \( 1 - 9 = -8 \)

Now, putting it all together, we get:

\(-x^2 + 3x - 8\)

Thus, the correct answer is:

D) (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8.