Question

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 \(7\).**