Question

Which example correctly demonstrates polynomial subtraction?(1 point) Responses (2x2+6x+1)−(3x2+3x+9)=x2+3x+8 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 6 x minus 4 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 4 right parenthesis (2x2+6x+1)−(3x2+3x+9)=5x2+9x+10 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals 5 x squared plus 9 x plus 10 (2x2+6x+1)−(3x2+3x+9)=−5x2+3x−8 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals 2 x squared plus 6 x plus 1 minus 3 x squared minus 3 x minus 9 (2x2+6x+1)−(3x2+3x+9)=−x2+3x−8

Answer 1

To determine which example correctly demonstrates polynomial subtraction, let's perform the polynomial subtraction step-by-step for the given expression:

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

To do this correctly, we can rewrite the expression as:

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

Now, let's combine like terms:
- For the \(x^2\) terms: \(2x^2 - 3x^2 = -1x^2\) or \(-x^2\),
- For the \(x\) terms: \(6x - 3x = 3x\),
- For the constant terms: \(1 - 9 = -8\).

Thus, the result of the subtraction is:

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

Now let's check the options you presented:

1. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8\) — Incorrect
2. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) — Incorrect
3. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8\) — Incorrect
4. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\) — **Correct**

Therefore, the correct example that demonstrates polynomial subtraction is:

\[
\boxed{-x^2 + 3x - 8}.
\]