Determine whether the expression is a polynomial, if it is state how many terms and variables the polynomial contains. state the degree
-4x-2y-1
the -2 and -1 are above the Y
If by that you mean you have negative exponents, then it is not a polynomial.
To determine whether an expression is a polynomial, we need to check a few criteria:
1. The expression must only contain variables, constants, and operations such as addition, subtraction, multiplication, and exponentiation.
2. The exponents of variables must be whole numbers or zero.
3. The variables in the expression must have non-negative exponents.
Let's analyze the given expression: -4x - 2y - 1.
1. The expression only contains variables (x and y), constants (-4, -2, and -1), and subtraction.
2. The exponents of the variables (x and y) are implicitly 1, which is a whole number.
3. The variables (x and y) do not have any exponents that violate the non-negative rule.
Therefore, the expression -4x - 2y - 1 qualifies as a polynomial.
Now, let's determine the number of terms and variables in this polynomial:
- The given expression has three terms: -4x, -2y, and -1.
- The expression contains two variables: x and y.
Lastly, let's find the degree of this polynomial. The degree of a polynomial is determined by the highest exponent of its variables. In this case, both x and y are raised to the power of 1. Therefore, the degree of this polynomial is 1.
In summary, the expression -4x - 2y - 1 is a polynomial with three terms and two variables (x and y), and it has a degree of 1.