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)ResponsesThe 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 −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 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 −12, and the last term is 7

Answer 1

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 first simplify the expression.

1. Distributing the negative sign in the second set of parentheses: \[ (12x^5 + 4x^4 + 9x^3 - 10x^2 + 15) - 24x^5 - 9x^3 + 7x^2 - 8 \]

2. Combine like terms:

   • For \(x^5\): \(12x^5 - 24x^5 = -12x^5\)
   • For \(x^4\): \(4x^4\) (no like terms)
   • For \(x^3\): \(9x^3 - 9x^3 = 0\) (these cancel each other)
   • For \(x^2\): \(-10x^2 + 7x^2 = -3x^2\)
   • For the constant term: \(15 - 8 = 7\)

3. Putting it all together, the simplified expression is: \[ -12x^5 + 4x^4 - 3x^2 + 7 \]

Now we identify the first and last terms:

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

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