Which example correctly demonstrates polynomial subtraction?(1 point)

Question

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:

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