Terms with Powers
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 38 of 64.
A polynomial is a sum of terms, where each term is a coefficient times a power of x. 4x^2 + x + 2x^2 is a polynomial. Its terms are 4x^2, x and 2x^2.
Polynomials are named by their number of terms. A monomial has one term, such as 3x^2. A binomial has two terms, such as x + 5. A trinomial has three terms, such as x^2 + 3x + 2. With more than three terms, the name is just polynomial. The prefix poly means many.
You simplify a polynomial by collecting like terms, the same as before. In 4x^2 + x + 2x^2, the terms 4x^2 and 2x^2 are like terms, so they add to 6x^2. The term x has a different power, so it stays on its own. The result is 6x^2 + x.
Challenge
MediumSimplify 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