Degree of a polynomial
Determine the degree of a polynomial in Grade 10 algebra. Find the monomial with the highest degree by summing variable exponents and use it to classify polynomials.
Key Concepts
The degree of a polynomial is the degree of its monomial with the greatest degree. The degree of a monomial is the sum of the exponents of its variable factors.
The degree of $7x^2y^4$ is $2+4=6$. For $ 2a^2b^3 + 4a^4b 9a^3$, the term degrees are 5, 5, and 3. The polynomial degree is 5. The polynomial $x^3 + x^7 2x^2$ has degree 7.
Think of it like a superhero team's power level! To find a polynomial's degree, first find the power level of each term by adding up the exponents on its variables. The biggest number you find is the polynomial's official degree, its highest rank. This tells you which term is the most powerful in the group.
Common Questions
What is the degree of a polynomial?
The degree of a polynomial is the highest degree among all its terms. The degree of each term is the sum of its variable exponents. For 3x²y + 5x³ - 2: degrees are 3, 3, and 0, so the polynomial is degree 3.
How do you find the degree of a monomial with multiple variables?
Add all the exponents of the variables in the monomial. For 4x²y³: degree = 2 + 3 = 5. For 7abc: degree = 1 + 1 + 1 = 3.
How does degree classify polynomials?
Degree 0 is a constant, degree 1 is linear, degree 2 is quadratic, degree 3 is cubic, degree 4 is quartic, degree 5 is quintic. The degree determines the maximum number of real roots.