Terms with Powers
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 38 of 64.
Bolt powers of x onto the terms you have collected since Fundamentals and you get the main object of the rest of this journey: the polynomial. 4x^2 + x + 2x^2 is one: a sum of terms, each a coefficient times a power of x.
Polynomials are named by their length. One term is a monomial (3x^2), two a binomial (x + 5), three a trinomial (x^2 + 3x + 2). Beyond three, "polynomial" covers everything: poly means many.
The tidying rule survives unchanged: like terms collect. 4x^2 and 2x^2 are like, six of the same thing together, and the lone x is not their kind: 6x^2 + x.
Challenge
MediumTidy 2x^2 + x + 5x^2 by collecting 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