Which of the following correctly identifies the first and last terms of the expression 4x3+3x−10+(2x−1)(−3x2+5)

Question

?(1 point)
Responses

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 .

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 4x3
. The last term is 5.

Answer 1

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

1. Start with the expression: \[ 4x^3 + 3x - 10 + (2x - 1)(-3x^2 + 5) \]

2. Next, expand \( (2x - 1)(-3x^2 + 5) \): \[ (2x)(-3x^2) + (2x)(5) + (-1)(-3x^2) + (-1)(5) \] This gives: \[ -6x^3 + 10x + 3x^2 - 5 \]

3. Now, combine this with the original expression: \[ 4x^3 + 3x - 10 - 6x^3 + 10x + 3x^2 - 5 \]

4. Combine like terms:

   • For \( x^3 \) terms: \( 4x^3 - 6x^3 = -2x^3 \)
   • For \( x^2 \) terms: \( 3x^2 \)
   • For \( x \) terms: \( 3x + 10x = 13x \)
   • For constant terms: \( -10 - 5 = -15 \)

5. The expression simplifies to: \[ -2x^3 + 3x^2 + 13x - 15 \]

Now we can identify the terms:

• The first term (highest degree) is \( -2x^3 \).
• The last term (constant) is \( -15 \).

So the correct identification is:

The first term is \( -2x^3 \). The last term is \( -15 \).

Thus, the correct response is:

• The first term is negative 2 x cubed. The last term is negative 15.