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 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 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.

Answer 1

To find 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 need to simplify the expression.

Distributing the negative sign to the second part of the expression:

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

This becomes:

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

Now, combine like terms:

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

2. For \(x^4\):
\[
4x^4 \quad \text{(no like terms)}
\]

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

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

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

Putting it all together, the simplified expression is:

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

Now, we can identify the first and last terms:

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

Thus, the correct response is:

**The first term is −12x^5, and the last term is 7.**