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.
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Start with the expression: \[ 4x^3 + 3x - 10 + (2x - 1)(-3x^2 + 5) \]
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Next, expand \( (2x - 1)(-3x^2 + 5) \): \[ (2x)(-3x^2) + (2x)(5) + (-1)(-3x^2) + (-1)(5) \] This gives: \[ -6x^3 + 10x + 3x^2 - 5 \]
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Now, combine this with the original expression: \[ 4x^3 + 3x - 10 - 6x^3 + 10x + 3x^2 - 5 \]
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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: \( -10 - 5 = -15 \)
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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.