Question

Which of the following correctly determines the first and last terms of the expression (12x^5+4x^4+9x^3−10x^2+15)−(24x^5+9x^3−7x^2+8)

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 will first simplify the expression by distributing the negative sign:

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

Next, we combine like terms:

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

2. For the \(x^4\) terms:
\[
4x^4
\]

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

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

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

Now we can write the simplified expression:

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

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

Thus, the first term is:
\(-12x^5\)

And the last term is:
\(7\)