To determine the degree of the polynomial [tex]\(2x^2 + 3x + 1\)[/tex], you need to identify the highest power of the variable [tex]\(x\)[/tex] in the polynomial.
Here are the steps to find the degree:
1. Identify the terms in the polynomial: The given polynomial is [tex]\(2x^2 + 3x + 1\)[/tex]. Each term in this polynomial is separated by a plus or minus sign. So, the terms are [tex]\(2x^2\)[/tex], [tex]\(3x\)[/tex], and [tex]\(1\)[/tex].
2. Determine the power of [tex]\(x\)[/tex] in each term:
- In the term [tex]\(2x^2\)[/tex], the power of [tex]\(x\)[/tex] is [tex]\(2\)[/tex].
- In the term [tex]\(3x\)[/tex], the power of [tex]\(x\)[/tex] is [tex]\(1\)[/tex].
- In the term [tex]\(1\)[/tex], there is no [tex]\(x\)[/tex], which means it can be considered as [tex]\(x^0\)[/tex], and thus the power of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
3. Identify the highest power: The powers of [tex]\(x\)[/tex] in the polynomial's terms are [tex]\(2\)[/tex], [tex]\(1\)[/tex], and [tex]\(0\)[/tex].
The highest power of the variable [tex]\(x\)[/tex] is [tex]\(2\)[/tex].
Thus, the degree of the polynomial [tex]\(2x^2 + 3x + 1\)[/tex] is:
[tex]\[ \boxed{2} \][/tex]
