To determine which of the given polynomial expressions have a degree of 2, we first need to understand what the degree of a polynomial is. The degree of a polynomial is the highest power of the variable [tex]\(x\)[/tex] in the expression.
Let's analyze each of the given polynomial expressions one by one:
1. [tex]\(3x^3 - 2\)[/tex]:
- The highest power of [tex]\(x\)[/tex] here is [tex]\(3\)[/tex].
- Degree = 3.
2. [tex]\(7x^2 + 5x - 1\)[/tex]:
- The highest power of [tex]\(x\)[/tex] here is [tex]\(2\)[/tex].
- Degree = 2.
3. [tex]\(2x^3 - x + 11\)[/tex]:
- The highest power of [tex]\(x\)[/tex] here is [tex]\(3\)[/tex].
- Degree = 3.
4. [tex]\(2x^4 - 35\)[/tex]:
- The highest power of [tex]\(x\)[/tex] here is [tex]\(4\)[/tex].
- Degree = 4.
5. [tex]\(x^2 + 9x - 10\)[/tex]:
- The highest power of [tex]\(x\)[/tex] here is [tex]\(2\)[/tex].
- Degree = 2.
6. [tex]\(x^4 + 2x^2 + 2\)[/tex]:
- The highest power of [tex]\(x\)[/tex] here is [tex]\(4\)[/tex].
- Degree = 4.
Now, we select all the expressions which have a degree of [tex]\(2\)[/tex]:
- [tex]\(7x^2 + 5x - 1\)[/tex]
- [tex]\(x^2 + 9x - 10\)[/tex]
Thus, the polynomial expressions with a degree of 2 are:
- [tex]\(7x^2 + 5x - 1\)[/tex]
- [tex]\(x^2 + 9x - 10\)[/tex]
