Which example correctly demonstrates polynomial subtraction?(1 point)

Question

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 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
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)=−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

Answer 1

To find the correct example of polynomial subtraction, we need to subtract the polynomial \( (3x^2 + 3x + 9) \) from \( (2x^2 + 6x + 1) \).

Let's perform the subtraction step by step:

1. Write the expression:

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

2. Distribute the negative sign across the second polynomial:

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

3. Combine like terms:

• For \( x^2 \) terms: \( 2x^2 - 3x^2 = -x^2 \)
• For \( x \) terms: \( 6x - 3x = 3x \)
• For constant terms: \( 1 - 9 = -8 \)

So the result is:

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

The correct statement is therefore:

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

From the provided options, the correct response is:

(2x² + 6x + 1) − (3x² + 3x + 9) = −x² + 3x − 8.