Question
Determine if the expression s, squared, plus, 6, square root of, s, end square root, minus, 9, s, to the power 4s
2
+6
s
−9s
4
is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
The given expression ______ a polynomial. The polynomial is a _____
and has a degree of ______.
2
+6
s
−9s
4
is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
The given expression ______ a polynomial. The polynomial is a _____
and has a degree of ______.
Answers
GPT-4o mini
To determine whether the expression \( s^2 + 6\sqrt{s} - 9s^4 \) is a polynomial, we first need to examine each term:
1. \( s^2 \) is a polynomial term with a degree of 2.
2. \( 6\sqrt{s} \) can be rewritten as \( 6s^{1/2} \), which is not a polynomial term because polynomials can only contain non-negative integer exponents.
3. \( -9s^4 \) is a polynomial term with a degree of 4.
Since one of the terms, \( 6\sqrt{s} \) or \( 6s^{1/2} \), is not a polynomial term, the overall expression cannot be classified as a polynomial.
Therefore, the given expression does **not** represent a polynomial.
The complete statement would be:
The given expression does not a polynomial.
1. \( s^2 \) is a polynomial term with a degree of 2.
2. \( 6\sqrt{s} \) can be rewritten as \( 6s^{1/2} \), which is not a polynomial term because polynomials can only contain non-negative integer exponents.
3. \( -9s^4 \) is a polynomial term with a degree of 4.
Since one of the terms, \( 6\sqrt{s} \) or \( 6s^{1/2} \), is not a polynomial term, the overall expression cannot be classified as a polynomial.
Therefore, the given expression does **not** represent a polynomial.
The complete statement would be:
The given expression does not a polynomial.