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Which of these polynomial expressions have a degree of 2? Select all that apply.

A. [tex]3x^3 - 2[/tex]
B. [tex]7x^2 + 5x - 1[/tex]
C. [tex]2x^3 - x + 11[/tex]
D. [tex]2x^4 - 35[/tex]
E. [tex]x^2 + 9x - 10[/tex]
F. [tex]x^4 + 2x^2 + 2[/tex]

Sagot :

GinnyAnsweridn
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]
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