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) ?(1 point)

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 need to simplify the expression by distributing the negative sign and combining like terms.

Starting with the original expression:

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

Distribute the negative to each term in the second polynomial:

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

Now, combine like terms:

1. **For \(x^5\)** terms: \(12x^5 - 24x^5 = -12x^5\)
2. **For \(x^4\)** terms: \(4x^4\) (there's no other \(x^4\) term)
3. **For \(x^3\)** terms: \(9x^3 - 9x^3 = 0\)
4. **For \(x^2\)** terms: \(-10x^2 + 7x^2 = -3x^2\)
5. **Constant terms**: \(15 - 8 = 7\)

Combining these results gives:

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

Now, we identify the first and last terms of this simplified polynomial.

- **First term** (the term with the highest degree): \(-12x^5\)
- **Last term** (the constant): \(7\)

Thus, the first term is \(-12x^5\) and the last term is \(7\).