Question

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

(2x2+6x+1)−(3x2+3x+9)=x2+3x+8
open paren 2 x squared plus 6 x plus 1 close paren minus open paren 3 x squared plus 3 x plus 9 close paren is equal to x squared plus 3 x plus 8

(2x2+6x+1)−(3x2+3x+9)=−x2+3x−8
open paren 2 x squared plus 6 x plus 1 close paren minus open paren 3 x squared plus 3 x plus 9 close paren is equal to negative x squared plus 3 x minus 8

(2x2+6x+1)−(3x2+3x+9)=−5x2+3x−8
open paren 2 x squared plus 6 x plus 1 close paren minus open paren 3 x squared plus 3 x plus 9 close paren is equal to negative 5 x squared plus 3 x minus 8

(2x2+6x+1)−(3x2+3x+9)=5x2+9x+10

Answer 1

To determine which option correctly demonstrates polynomial subtraction, we will calculate the expression \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\) step-by-step.

1. Distribute the negative sign in the second polynomial:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

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

3. Putting it all together, we have:
\[
-x^2 + 3x - 8
\]

Now, let's compare our result with the provided options:

- The first option is \(x^2 + 3x + 8\): Incorrect
- The second option is \(-x^2 + 3x - 8\): Correct
- The third option is \(-5x^2 + 3x - 8\): Incorrect
- The fourth option is \(5x^2 + 9x + 10\): Incorrect

Hence, the correct response demonstrating polynomial subtraction is:

**(2x²+6x+1)−(3x²+3x+9)=−x²+3x−8**.