Sure, let's determine the degree of the polynomial [tex]\(5x - 3x^2 - 1 + 7x^3\)[/tex].
To find the degree of a polynomial, we examine the term with the highest exponent of [tex]\(x\)[/tex].
Here are the terms of the polynomial:
1. [tex]\(5x\)[/tex] - The exponent here is 1.
2. [tex]\(-3x^2\)[/tex] - The exponent here is 2.
3. [tex]\(-1\)[/tex] - This is a constant term, which can be thought of as [tex]\(x^0\)[/tex], so the exponent is 0.
4. [tex]\(7x^3\)[/tex] - The exponent here is 3.
The highest exponent among these terms is [tex]\(3\)[/tex] (from the term [tex]\(7x^3\)[/tex]).
Therefore, the degree of the polynomial [tex]\(5x - 3x^2 - 1 + 7x^3\)[/tex] is [tex]\(3\)[/tex].
So, the correct answer is:
(3) 3
