Identify the Degree of a Polynomial

Supplied materials

• Paper or a browser scratch area; a calculator is optional unless rounding is requested.
• Supplied teaching case: What is the degree of 2x^4−3x²+6? Candidate answers: (A) 2 (B) 3 (C) 4 (D) 6.
• Independent check inputs: What is the degree of 3x^5−4x²+7? Candidate answers: (A) 2 (B) 3 (C) 5 (D) 7.

Learn the idea

Polynomials combine terms with nonnegative integer variable powers. Their degree describes the highest power, while addition, multiplication and factoring preserve equivalent expressions that can be checked by expansion or substitution. Degree is determined by the greatest variable exponent attached to a nonzero coefficient. Coefficients scale terms without changing their degree, and constants have degree zero when nonzero.

Here is the method on the supplied teaching case. The largest exponent with a nonzero coefficient is 4. Coefficient size and the number of terms do not determine degree.

The number of terms is not the degree. Inspect exponents after simplifying any canceling terms; here the stated leading coefficient is nonzero, so its highest-power term remains present.

1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
3. Solve the independent check with its changed inputs before revealing feedback.
4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Check your reasoning

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Take it further

Changed-input task: What is the degree of 9x^11−10x²+13? Candidate answers: (A) 11 (B) 2 (C) 3 (D) 9. Show the mathematical reason, not only the selected answer. Expected result: 11. The largest exponent with a nonzero coefficient is 11. Coefficient size and the number of terms do not determine degree.

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