Polynomial — Definition and Degree

Check each term, note the power of the variable, ensure the powers are non-negative whole numbers, and then choose the highest power as the degree.

A term table can be used with columns for term, coefficient, power of variable, and role in expression.

For 7x³ + 2x² + 5, a common wrong answer is degree 7 because students look at the largest coefficient instead of the largest exponent.

A polynomial is an algebraic expression made using variables, constants, coefficients, and non-negative whole number powers of variables. The degree is the highest power of the variable present in the polynomial.

A polynomial is an algebraic expression made using variables, constants, coefficients, and non-negative whole number powers of variables. The degree is the highest power of the variable present in the polynomial. Polynomial rule: powers of variables must be non-negative whole numbers. Degree in one variable is the highest exponent of the variable. In 5x³ - 2x + 8, the highest power of x is 3, so the degree is 3. In 4x + 9, the degree is 1, so it is linear.

In one variable, expressions like 3x + 2, x² - 5x + 6, and 7 are polynomials because the powers of x are whole numbers. Expressions with variables in the denominator or square root of the variable are not polynomials at this level. The degree tells the type of polynomial, such as linear for degree 1 and quadratic for degree 2. Polynomial rule: powers of variables must be non-negative whole numbers. Degree in one variable is the highest exponent of the variable. Find the degree of 9 - 3x + 2x⁴. The powers of x are 0 for 9, 1 for -3x, and 4 for 2x⁴. The highest power is 4, so the degree is 4. Students may be asked to identify whether an expression is a polynomial, find its degree, or classify it as constant, linear, quadratic, or higher degree. For 7x³ + 2x² + 5, a common wrong answer is degree 7 because students look at the largest coefficient instead of the largest exponent.