Question

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

(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)=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)=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 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

(2x2+6x+1)−(3x2+3x+9)=−x2+3x−8

Answer 1

To determine which example correctly demonstrates polynomial subtraction, let's evaluate each option:

1. **Option 1:**
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8\)

Subtraction:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
Combine like terms:
\[
(2x^2 - 3x^2) + (6x - 3x) + (1 - 9) = -x^2 + 3x - 8
\]
**This does not match the result provided.**

2. **Option 2:**
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10\)

Using the same subtraction:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]
**This does not match the result provided.**

3. **Option 3:**
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8\)

Using the same subtraction:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]
**This does not match the result provided.**

4. **Option 4:**
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\)

Using the same subtraction:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]
**This matches the result provided.**

Therefore, **Option 4** is the correct example that demonstrates polynomial subtraction.