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Which example correctly demonstrates polynomial subtraction? (1 point)

• (2x2 + 6x + 1) - (3x2 + 3x + 9) = 5x2 + 9x + 10
• (2x" + 6x + 1) - (3x2 + 3x + 9) = -x2 + 3x - 8
• (2x2 + 6x + 1) - (3x2 + 3х + 9) = - 5x2 + 3х - 8
• (2x2 + 6x + 1) - (3x2 + 3x + 9) = x2 + 3x + 8

1 answer

To determine which example correctly demonstrates polynomial subtraction, we need to perform the subtraction for each case.

The expression is: \[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) \]

This can be simplified as follows:

  1. Distribute the negative sign: \[ = 2x^2 + 6x + 1 - 3x^2 - 3x - 9 \]

  2. Combine like terms:

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

So we have: \[ -1x^2 + 3x - 8 \text{ or } -x^2 + 3x - 8 \]

Now, let's analyze the provided options:

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

    • This is incorrect.

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

    • This is correct.

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

    • This is incorrect.

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

    • This is incorrect.

Thus, the correct answer is: \[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8 \]