The Degree
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 39 of 64.
The degree of a polynomial is the largest exponent on x once the expression is tidy. x^2 + 3x + 2 has degree 2; 5x^7 - x has degree 7. Degree is the polynomial's headline number: it drives the shape of its graph and the difficulty of its equations, as the coming sections will show.
"Once the expression is tidy" is doing real work in that sentence. x * x^2 + x^3 looks like its biggest exponent is 3, but the first term is hiding one: x * x^2 = x^3 by the product rule. Tidied, the expression is 2x^3, a degree 3 monomial.
Standard practice writes a tidy polynomial in standard form, largest exponent first: x^2 + 3x + 2, not 2 + 3x + x^2. The degree then sits in front, announcing itself.
Challenge
MediumTidy x * x^3 + x^4.
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