To identify the first and last terms of the expression \( 4x^3 + 3x - 10 + (2x - 1)(-3x^2 + 5) \), we need to first simplify the expression by expanding the product \( (2x - 1)(-3x^2 + 5) \).
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Expand the expression:
\[ (2x - 1)(-3x^2 + 5) = 2x(-3x^2) + 2x(5) - 1(-3x^2) - 1(5) \] \[ = -6x^3 + 10x + 3x^2 - 5 \] \[ = -6x^3 + 3x^2 + 10x - 5 \]
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Combine this with the original expression:
Now we combine this result with the rest of the original expression: \[ 4x^3 + 3x - 10 + (-6x^3 + 3x^2 + 10x - 5) \] Grouping similar terms: \[ = (4x^3 - 6x^3) + 3x^2 + (3x + 10x) + (-10 - 5) \] \[ = -2x^3 + 3x^2 + 13x - 15 \]
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Identify the first and last terms:
The final expression is: \[ -2x^3 + 3x^2 + 13x - 15 \]
- The first term (the term with the highest power of \(x\)) is \( -2x^3 \).
- The last term (the constant term) is \( -15 \).
So, the first term is \( -2x^3 \) and the last term is \( -15 \).
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