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 negative x squared plus 3 x minus 8 (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

Let's perform the polynomial subtraction for the expression \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\).

1. Start with the original expression:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]

2. Distribute the negative sign across the terms in the second polynomial:
\[
2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

3. 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: \(1 - 9 = -8\)

4. Putting it all together:
\[
-x^2 + 3x - 8
\]

This simplifies to:
\[
-x^2 + 3x - 8
\]

Thus, the correct example demonstrating polynomial subtraction is:

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

So the first response is correct:
\[
\text{(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8}
\]