Question

Which example correctly demonstrates polynomial subtraction?

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

Answer 1

To perform polynomial subtraction, we need to distribute the negative sign to the terms in the second polynomial before combining like terms.

Let's subtract the polynomials step by step:

\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]

Distributing the negative sign gives us:

\[
2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

Now, we combine the like terms:

- For \(x^2\) terms: \(2x^2 - 3x^2 = -1x^2\) or \(-x^2\)
- For \(x\) terms: \(6x - 3x = 3x\)
- For constant terms: \(1 - 9 = -8\)

Putting it all together, we find:

\[
-x^2 + 3x - 8
\]

Thus, the correct answer is:

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