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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)=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+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

1 answer

To determine which example correctly demonstrates polynomial subtraction, we need to perform the subtraction step-by-step for the expression \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\).

  1. Rewrite the expression for clarity: \[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 2x^2 + 6x + 1 - 3x^2 - 3x - 9 \]

  2. Combine the 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: \[ -1x^2 + 3x - 8 \]

Now, looking through the provided responses:

  1. First response: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8\) (Incorrect)
  2. Second response: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8\) (Incorrect)
  3. Third response: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\) (Correct)
  4. Fourth response: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) (Incorrect)

Thus, the correct example that demonstrates polynomial subtraction is: (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8.