Degree of a monomial
Find the degree of a monomial in Grade 9 algebra by summing all variable exponents: x²y³ has degree 5, a constant has degree 0, used to classify polynomials in Saxon Algebra 1.
Key Concepts
Property The degree of a monomial is the sum of the exponents of the variables in the monomial. A constant has a degree of 0.
Examples The degree of $8a^3b^6c$ is $3 + 6 + 1 = 10$. Remember that $c$ is the same as $c^1$. The degree of $15x^4y^5z^2$ is $4 + 5 + 2 = 11$. Just sum the variable exponents! The degree of $50^2x^5y^3$ is $5 + 3 = 8$. The exponent on the number $50$ is a trap; ignore it!
Explanation Think of this as finding the 'power level' of a term! To find the degree, you simply add up the exponents of all the variables. Be careful to ignore any exponents on the coefficients (the numbers in front). The game is all about counting the total power of the variables, nothing else matters for the degree!
Common Questions
How do you find the degree of a monomial?
Add up the exponents of all variables in the monomial. For x²y³, the degree is 2 + 3 = 5. For 7x⁴, the degree is 4. A constant like 8 has degree 0 since there are no variables.
What is the degree of the monomial -4x³y²z?
Add the exponents of x, y, and z: 3 + 2 + 1 = 6. The degree is 6. Remember that z without a written exponent has exponent 1. The coefficient -4 does not affect the degree.
How is the degree of a monomial used in classifying polynomials?
The degree of a polynomial equals the highest degree among all its monomial terms. A polynomial with highest degree 1 is linear, degree 2 is quadratic, degree 3 is cubic. This classification determines the shape of the graph.