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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.
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.
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