Question

Which example correctly demonstrates polynomial subtraction?(1 point)
Responses

(2x^2+6x+1)−(3x^2+3x+9)=5x^2+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

(2x^2+6x+1)−(3x^2+3x+9)=x^2+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

(2x^2+6x+1)−(3x^2+3x+9)=−x^2+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

(2x^2+6x+1)−(3x^2+3x+9)=−5x^2+3x−8

Answer 1

To determine the correct demonstration of polynomial subtraction, let's perform the subtraction step by step:

We need to calculate:

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

First, distribute the negative sign to the second polynomial:

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

Now, combine like terms:

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

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

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

Putting it all together, we get:

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

Now we can check the given options:

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

The correct answer is:

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