Definition: The degree of a polynomial is the highest exponent found on its variable once like terms are combined; for several variables, it is the largest sum of exponents in one term.
How do you find the degree?
Look at each term and note its exponent. The largest one is the degree. A constant such as 9 has degree 0. A linear polynomial has degree 1, a quadratic has degree 2, and a cubic has degree 3.
Why does it matter?
The degree predicts the shape of the graph and the greatest number of zeros the polynomial can have. A degree 3 polynomial crosses the x-axis at most three times.
Example. The polynomial 5x2 + 8x6 – 3x + 4 has degree 6, even though the 5x2 term is written first. For a term with two variables, such as 7x3y2, add the exponents: 3 + 2 = 5, so this term has degree 5.
Which mistakes appear?
Students take the first term’s exponent instead of the largest. Others forget to simplify first: (x4 + 2x) – x4 equals 2x, so the degree is 1, not 4. And the number zero is a special case with no defined degree.