Question
Determine if the expression minus, 3, r, squared, minus, start fraction, r, to the power 4 , divided by, 6, end fraction−3r
2
−
6
r
4
is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
Answer
Attempt 2 out of 5
The given expression represents a polynomial. The polynomial is a _______
and has a degree of _____.
2
−
6
r
4
is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
Answer
Attempt 2 out of 5
The given expression represents a polynomial. The polynomial is a _______
and has a degree of _____.
Answers
GPT-4o mini
The given expression is \(-3r^2 - \frac{r^4}{6} - 3r\).
To determine if this expression is a polynomial, we need to check if it meets the criteria for being a polynomial:
1. A polynomial is an expression that involves variables raised to non-negative integer powers.
2. It can include constants, but cannot include variables in the denominator or variables with negative or fractional exponents.
In the given expression:
- \(-3r^2\) is a polynomial term of degree 2.
- \(-\frac{r^4}{6}\) is a polynomial term of degree 4, which is still valid as it is a non-negative integer exponent.
- \(-3r\) is a polynomial term of degree 1.
Since all terms have non-negative integer exponents and there are no variables in the denominator, the expression is indeed a polynomial.
Next, we determine the type and degree of the polynomial:
- The polynomial is a **multinomial** (because it has more than one term).
- The degree of the polynomial is determined by the highest degree of its individual terms, which in this case is 4 (from the term \(-\frac{r^4}{6}\)).
Therefore, we can fill in the blanks:
The given expression represents a polynomial. The polynomial is a **multinomial** and has a degree of **4**.
To determine if this expression is a polynomial, we need to check if it meets the criteria for being a polynomial:
1. A polynomial is an expression that involves variables raised to non-negative integer powers.
2. It can include constants, but cannot include variables in the denominator or variables with negative or fractional exponents.
In the given expression:
- \(-3r^2\) is a polynomial term of degree 2.
- \(-\frac{r^4}{6}\) is a polynomial term of degree 4, which is still valid as it is a non-negative integer exponent.
- \(-3r\) is a polynomial term of degree 1.
Since all terms have non-negative integer exponents and there are no variables in the denominator, the expression is indeed a polynomial.
Next, we determine the type and degree of the polynomial:
- The polynomial is a **multinomial** (because it has more than one term).
- The degree of the polynomial is determined by the highest degree of its individual terms, which in this case is 4 (from the term \(-\frac{r^4}{6}\)).
Therefore, we can fill in the blanks:
The given expression represents a polynomial. The polynomial is a **multinomial** and has a degree of **4**.