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Which of the following correctly determines the first and last terms of the expression (12x5+4x4+9x3−10x2+15)−(24x5+9x3−7x2+8) ?(1 point) Responses The first term is 12x5, and the last term is −7. The first term is 12 x superscript 5 baseline , and the last term is negative 7 . The first term is −12x5, and the last term is 7. The first term is negative 12 x superscript 5 baseline , and the last term is 7. The first term is 4x4 , and the last term is −3x2. The first term is 4 x superscript 4 baseline , and the last term is negative 3 x squared . The first term is −12, and the last term is 7

1 answer

To determine the first and last terms of the expression \((12x^5 + 4x^4 + 9x^3 - 10x^2 + 15) - (24x^5 + 9x^3 - 7x^2 + 8)\), we can simplify the expression step by step.

First, we'll distribute the negative sign to the second group of terms:

\[ 12x^5 + 4x^4 + 9x^3 - 10x^2 + 15 - 24x^5 - 9x^3 + 7x^2 - 8 \]

Now, combine like terms:

  1. The \(x^5\) terms: \[ 12x^5 - 24x^5 = -12x^5 \]

  2. The \(x^4\) term: \[ 4x^4 (no other x^4 terms) \]

  3. The \(x^3\) terms: \[ 9x^3 - 9x^3 = 0 \]

  4. The \(x^2\) terms: \[ -10x^2 + 7x^2 = -3x^2 \]

  5. The constant terms: \[ 15 - 8 = 7 \]

Putting it all together, we have:

\[ -12x^5 + 4x^4 - 3x^2 + 7 \]

In this expression:

  • The first term (the one with the highest degree) is \(-12x^5\).
  • The last term (the constant term) is \(7\).

So the correct response is:

The first term is \(-12x^5\), and the last term is \(7\).