Question

Which example correctly demonstrates polynomial subtraction? (1 point)
$(2x^{2}+6x+1)-(3x^{2}+3x+9)=-x^{2}+3x-8$
$(2x^{2}+6x+1)-(3x^{2}+3x+9)=-5x^{2}+3x-8$
$(2x^{2}+6x+1)-(3x^{2}+3x+9)=x^{2}+3x+8$
$(2x^{2}+6x+1)-(3x^{2}+3x+9)=5x^{2}+9x+10$

Answer 1

To check which example correctly demonstrates polynomial subtraction, we need to perform the subtraction on the given polynomials:

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

We can distribute the negative sign into the second polynomial:

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

Now, we can group the like terms together:

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

Calculating each group:

1. For the \(x^2\) terms:
\[
2x^2 - 3x^2 = -1x^2 \text{ or } -x^2.
\]

2. For the \(x\) terms:
\[
6x - 3x = 3x.
\]

3. For the constant terms:
\[
1 - 9 = -8.
\]

Putting it all together, we have:

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

Now we compare this result with the provided answer choices:

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

The first option matches our result exactly. Therefore, the correct example that demonstrates polynomial subtraction is:

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