Determine if the expression 4m^5-6m^8 is a polynomial in one variable. If so, state the degree.
I really don't understand how to do this, and I can find it in my pre-calculus book.
There is only one variable, m
There is more than one term, one in m^5 and one in m^8, so it is polynomial not monomial.
The highest degree is 8 so it is of eighth degree.
To determine if an expression is a polynomial in one variable, we need to check two things:
1. The expression must have a finite number of terms.
2. Each term must have a variable raised to a non-negative integer exponent.
Let's analyze the given expression, 4m^5 - 6m^8, step by step:
1. The expression consists of two terms: 4m^5 and -6m^8, so it has a finite number of terms.
2. In the first term, 4m^5, the variable m is raised to the power of 5, which is a non-negative integer exponent.
3. In the second term, -6m^8, the variable m is raised to the power of 8, which is also a non-negative integer exponent.
Since both terms have the variable m raised to non-negative integer exponents, the expression 4m^5 - 6m^8 is indeed a polynomial in one variable, namely m.
Now, to determine the degree of the polynomial, we consider the highest power (exponent) of the variable in the polynomial. In this case, the highest power is 8 (from the term -6m^8).
Therefore, the degree of the polynomial 4m^5 - 6m^8 is 8.
I hope this explanation helps! Let me know if you have any further questions.
To determine if an expression is a polynomial in one variable, we need to make sure that the powers of the variable are whole numbers, and there are no variables in the denominators or inside any radicals.
In the given expression, 4m^5 - 6m^8, we have only one variable, which is 'm'. The powers of 'm' are 5 and 8, both of which are whole numbers. So, the powers in the expression satisfy the first condition.
Next, we need to check for any variables in the denominators or inside radicals. In this expression, we do not have any divisions involving 'm' and there are no radicals containing 'm' either.
Therefore, we can conclude that the expression 4m^5 - 6m^8 is indeed a polynomial in one variable, which is 'm'.
Now, to determine the degree of the polynomial, we look at the term with the highest power of 'm'. In this case, it is -6m^8. The degree of a polynomial is equal to the power of the term with the highest exponent.
So, the degree of the given polynomial 4m^5 - 6m^8 is 8.