Question

Exponents & Radicals Unit Test
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Question
Which of the following correctly identifies the first and last terms of the expression 4x3+3x−10+(2x−1)(−3x2+5)
?(1 point)
Responses

The first term is 4x3
. The last term is 5.
The first term is 4 x cubed . The last term is 5.

The first term is −2x3
. The last term is −15
.
The first term is negative 2 x cubed . The last term is negative 15 .

The first term is −2x3
. The last term is −10
.
The first term is negative 2 x cubed . The last term is negative 10 .

The first term is 4x3
. The last term is −5
.
The first term is 4 x cubed . The last term is negative 5 .
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Answer 1

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

1. **Distributing (2x - 1) with (-3x² + 5)**:
\[
(2x)(-3x^2) + (2x)(5) + (-1)(-3x^2) + (-1)(5)
\]
\[
= -6x^3 + 10x + 3x^2 - 5
\]

2. **Now add this to the original expression:**
\[
4x^3 + 3x - 10 + (-6x^3 + 10x + 3x^2 - 5)
\]
Combine like terms:
- For \(x^3\): \( 4x^3 - 6x^3 = -2x^3 \)
- For \(x^2\): \( 0 + 3x^2 = 3x^2 \)
- For \(x\): \( 3x + 10x = 13x \)
- Constant terms: \( -10 - 5 = -15 \)

Putting it all together gives:
\[
-2x^3 + 3x^2 + 13x - 15
\]

From the simplified expression \( -2x^3 + 3x^2 + 13x - 15 \):
- The **first term** is \( -2x^3 \).
- The **last term** is \( -15 \).

The correct response is:
**The first term is −2x³. The last term is −15.**