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

Answer 1

Let's break down the polynomial subtraction step by step for the expression \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\).

1. Write down the polynomials:

   • First polynomial: \(2x^2 + 6x + 1\)
   • Second polynomial: \(3x^2 + 3x + 9\)

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

3. Combine like terms:

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

4. Write down the result: \[ -1x^2 + 3x - 8 \]

So the correct expression for the polynomial subtraction is: \[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8 \]

The expression provided in your question, \(5x^2 + 9x + 10\), is incorrect. The correct result from the subtraction is \(-x^2 + 3x - 8\).