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)
Responses

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.
The first term is negative 12 , 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 .

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 need to simplify the expression.

1. Distribute the negative sign across 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 \(x^5\) terms: \(12x^5 - 24x^5 = -12x^5\)
- For \(x^4\) terms: \(4x^4\) (there's no other x^4 term)
- For \(x^3\) terms: \(9x^3 - 9x^3 = 0\)
- For \(x^2\) terms: \(-10x^2 + 7x^2 = -3x^2\)
- For the constant terms: \(15 - 8 = 7\)

3. Now write the simplified expression:
\[
-12x^5 + 4x^4 - 3x^2 + 7
\]

From this result:
- The first term (the term with the highest degree) 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.**