The Degree
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 39 of 64.
The degree of a polynomial in x is the largest exponent of x after the polynomial is simplified. The polynomial x^2 + 3x + 2 has degree 2, and 5x^7 - x has degree 7.
Simplify any products and collect the like terms before you read the degree. For example, x × x^2 + x^3 = x^3 + x^3 = 2x^3. The result is a monomial of degree 3.
Standard form lists the terms from the largest exponent down to the smallest. For example, 2 + 3x + x^2 in standard form is x^2 + 3x + 2. In standard form, the exponent of the first term is the degree.
Challenge
MediumSimplify x × x^3 + x^4 and collect the like terms.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Exponents & Polynomials
1What a Power Is
Repeated MultiplicationSquares and CubesPowers of Negative NumbersWhere the Minus LivesRecap: First Powers4Power of a Power
A Power Raised AgainWhy Exponents MultiplyProduct Rule or Power Rule?The Rule in LettersRecap: Power of a Power2The Product Rule
Multiplying Same BasesWith CoefficientsMore Than Two FactorsThe Rule in LettersRecap: The Product Rule5Product and Quotient Powers
Every Factor Gets the PowerWith a Number InsideA Power of a QuotientAll Three Rules TogetherRecap: Products and Quotients8What a Polynomial Is
Terms with PowersThe DegreeLike Terms, Only StrongerRecap: Meet the Polynomials11Dividing by a Monomial
Splitting the FractionDividing by a Variable TermBigger SplitsCancel with CareRecap: Dividing3The Quotient Rule
Dividing Same BasesWhy Exponents SubtractWith CoefficientsThe Rule in LettersRecap: The Quotient Rule6Zero and Negative Exponents
The Zero ExponentZero at WorkNegative Means ReciprocalWriting Without NegativesPowers of TenRecap: Zero and Negative