Question

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

(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 negative x squared plus 3 x minus 8

(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)=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)=−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

Answer 1

To demonstrate polynomial subtraction correctly, we start by handling the expression piece by piece.

The expression we need to evaluate is:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]

Step 1: Distribute the negative sign across the second polynomial:
\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

Step 2: Combine like terms:
- Combine \(2x^2\) and \(-3x^2\):
\[
2x^2 - 3x^2 = -x^2
\]

- Combine \(6x\) and \(-3x\):
\[
6x - 3x = 3x
\]

- Combine \(1\) and \(-9\):
\[
1 - 9 = -8
\]

Putting it all together:
\[
-x^2 + 3x - 8
\]

Now, let's evaluate the provided options to find the correct demonstration of polynomial subtraction.

1. **First option**: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\) (Correct)
2. **Second option**: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8\) (Incorrect)
3. **Third option**: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) (Incorrect)
4. **Fourth option**: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8\) (Incorrect)

The **first option** is the correct example of polynomial subtraction.