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