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 x squared plus 3 x plus 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 minus 5 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 negative x squared plus 3 x minus 8

(2x2+6x+1)−(3x2+3x+9)=5x2+9x+10

Answer 1

To perform polynomial subtraction correctly, you need to distribute the negative sign across the polynomial being subtracted, and then combine like terms.

Let's break down the subtraction step by step:

1. Start with the original expression: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\)

2. Apply the subtraction: \((2x^2 + 6x + 1) - 3x^2 - 3x - 9\)

3. Now combine like terms:

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

Putting it all together, the result is: \(-x^2 + 3x - 8\)

Now, let's look at each provided response:

1. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8\) (Incorrect)
2. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8\) (Incorrect)
3. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\) (Correct)
4. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) (Incorrect)

The correct response is: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\).