Which example correctly demonstrates polynomial subtraction?(1 point)%0D%0AResponses%0D%0A%0D%0A(2x2+6x+1)−(3x2+3x+9)=−5x2+3x−8%0D%0Aleft 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%0D%0A%0D%0A(2x2+6x+1)−(3x2+3x+9)=−x2+3x−8%0D%0Aleft 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%0D%0A%0D%0A(2x2+6x+1)−(3x2+3x+9)=5x2+9x+10%0D%0Aleft 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%0D%0A%0D%0A(2x2+6x+1)−(3x2+3x+9)=x2+3x+8

To correctly demonstrate polynomial subtraction, we need to perform the operation step-by-step. Let's take the polynomial subtraction:

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

We can distribute the negative sign to the second polynomial:

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

Now, combine like terms:

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

Putting these together, we have:

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

Now, let's compare this result with the given options:

1. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8\) (incorrect)
2. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\) (correct)
3. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) (incorrect)
4. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8\) (incorrect)

The correct example that demonstrates polynomial subtraction is the second one:

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