High School

Which algebraic expression is a polynomial with a degree of [tex]$4$[/tex]?

A. [tex]5x^4[/tex]

B. [tex]x^5 - 6x^4 + 14x^3 + x^2[/tex]

C. [tex]9x^4 - x^3[/tex]

D. [tex]2x^4 - 6x^4[/tex]

Answer :

To determine which algebraic expression is a polynomial with a degree of 4, we need to analyze each given expression and identify the highest degree of the variable [tex]\(x\)[/tex].

1. Expression 1: [tex]\(5x^4\)[/tex]
- This expression consists of a single term [tex]\(5x^4\)[/tex].
- The degree of this term is 4.

2. Expression 2: [tex]\(x^5 - 6x^4 + 14x^3 + x^2\)[/tex]
- This expression has terms with degrees: 5, 4, 3, and 2.
- The highest degree is 5 due to the term [tex]\(x^5\)[/tex].

3. Expression 3: [tex]\(9x^4 - x^3\)[/tex]
- This expression has terms with degrees: 4 and 3.
- The highest degree is 4 because of the term [tex]\(9x^4\)[/tex].

4. Expression 4: [tex]\(2x^4 - 6x^4\)[/tex]
- Combine the terms: [tex]\((2x^4) - (6x^4) = -4x^4\)[/tex].
- The resulting expression is [tex]\(-4x^4\)[/tex], with a degree of 4.

Now, let's identify which of these expressions are polynomials of degree 4:

- Expression 1: [tex]\(5x^4\)[/tex] is a polynomial with degree 4.
- Expression 3: [tex]\(9x^4 - x^3\)[/tex] is a polynomial with degree 4.
- Expression 4: [tex]\(-4x^4\)[/tex] is a polynomial with degree 4.

Hence, the polynomials with a degree of 4 are from Expression 1, Expression 3, and Expression 4.