Question

Which of the following correctly identifies the first and last terms of the expression 4x^3+3x−10+(2x−1)(−3x^2+5) ?

Answer 1

To identify the first and last terms of the expression \( 4x^3 + 3x - 10 + (2x - 1)(-3x^2 + 5) \), we need to first simplify the expression by expanding the product \( (2x - 1)(-3x^2 + 5) \).

1. **Expand the expression:**

\[
(2x - 1)(-3x^2 + 5) = 2x(-3x^2) + 2x(5) - 1(-3x^2) - 1(5)
\]
\[
= -6x^3 + 10x + 3x^2 - 5
\]
\[
= -6x^3 + 3x^2 + 10x - 5
\]

2. **Combine this with the original expression:**

Now we combine this result with the rest of the original expression:
\[
4x^3 + 3x - 10 + (-6x^3 + 3x^2 + 10x - 5)
\]
Grouping similar terms:
\[
= (4x^3 - 6x^3) + 3x^2 + (3x + 10x) + (-10 - 5)
\]
\[
= -2x^3 + 3x^2 + 13x - 15
\]

3. **Identify the first and last terms:**

The final expression is:
\[
-2x^3 + 3x^2 + 13x - 15
\]

- The **first term** (the term with the highest power of \(x\)) is \( -2x^3 \).
- The **last term** (the constant term) is \( -15 \).

So, the first term is \( -2x^3 \) and the last term is \( -15 \).