To perform the operation \( (8x^2 + 7x - 1) - (2x^2 - 5x) - (-5x^3 - 4x^2 + 3) \), we will first distribute the negative signs and then combine like terms.
Step 1: Rewrite the expression with distributed negative signs:
\[ (8x^2 + 7x - 1) - (2x^2 - 5x) + (5x^3 + 4x^2 - 3) \]
Step 2: Combine like terms:
Let's group the terms by degree:
-
For \(x^3\):
- \(5x^3\)
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For \(x^2\):
- \(8x^2 - 2x^2 + 4x^2 = (8 - 2 + 4)x^2 = 10x^2\)
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For \(x\):
- \(7x + 5x = 12x\)
-
Constant terms:
- \(-1 + 3 = 2\)
Step 3: Combine everything together:
Putting it all together, we have:
\[ 5x^3 + 10x^2 + 12x + 2 \]
Step 4: Identify the degree of the polynomial:
The degree of the polynomial is the highest degree of its terms, which is 3 (from the term \(5x^3\)).
Thus, the final answer in standard form is:
\[ \boxed{5x^3 + 10x^2 + 12x + 2} \]
And its degree is:
\[ \boxed{3} \]
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