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How do you find the degree of a polynomial?

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Quick Answer

To find the degree of a polynomial expression, look at each of the terms to find the one with the most exponents, counting by power rather than by constant. The number of polynomials in the term with the most is the degree of that polynomial expression.

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Full Answer

  1. Look at all of the terms in the polynomial expression

    Consider the example 4x^4 + x^3 + 2x^2 - 5x - 1. Look for exponents associated with variables; four of the terms have exponents. Look at the first term, which has four exponents; this comes from the fact that x is raised to the fourth power, not that x^4 is multiplied by 4.

  2. Follow the same process for expressions with multiple variables.

    Consider the example 2xy^4 + 3x^2y - 8xy^2 - 4x + 3. Count the exponents in each of the terms, going by exponent rather than the multiplying constant. Look at the first term, which has five exponents (x raised to the first power and y raised to the fourth power).

  3. Identify the degree for each polynomial

    Look at the example in Step 1 again. Write the greatest number of exponents in one term (4) down as the degree of that polynomial. Look at the example in Step 2 again. Write the greatest number of exponents in one term (5) as the degree of that polynomial. Remember that the exponents indicate the number of polynomials in a term -- and the degree, if that term has the most polynomials.

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