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 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 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 −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 by distributing the negative sign:

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

Now, we combine like terms:

- For \(x^5\): \(12x^5 - 24x^5 = -12x^5\)
- For \(x^4\): \(4x^4\) (there's nothing to combine it with)
- For \(x^3\): \(9x^3 - 9x^3 = 0\) (these terms cancel out)
- For \(x^2\): \(-10x^2 + 7x^2 = -3x^2\)
- For the constant terms: \(15 - 8 = 7\)

Putting it all together, we have:

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

Now we can identify the first and last terms:
- The first term (the term with the highest degree) is \(-12x^5\).
- The last term (the constant) is \(7\).

So, the correct answer is:
**The first term is -12x^5, and the last term is 7.**