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 −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.

1 answer

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.
Similar Questions
    1. answers icon 1 answer
  1. Exponents & Radicals Unit Test9 of 199 of 19 Items Question Which of the following correctly identifies the first and last terms
    1. answers icon 1 answer
    1. answers icon 1 answer
  2. ANSWER ALL OF THE QUESTIONS CORRECTLY.Answer the following give the expression. Answer options may be used more than once or not
    1. answers icon 1 answer
more similar questions