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 negative x squared plus 3 x minus 8 (2x2+6x+1)−(3x2+3x+9)=x2+3x+8

Answer 1

To find the correct polynomial subtraction, we need to subtract the second polynomial from the first polynomial step by step.

Let's perform the subtraction:

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

Distributing the negative sign across the second polynomial yields:

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

Now, we combine like terms:

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

Putting it all together, we have:

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

Therefore, the correct response that demonstrates polynomial subtraction is:

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

This matches the option:

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