Adding Polynomials
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 42 of 64.
Adding two polynomials is nothing new: drop the parentheses and collect like terms. 3x^2 + 2x + (x^2 - 5x): a plus sign in front of a parenthesis changes nothing inside, so the terms pour out as they are, 3x^2 + 2x + x^2 - 5x.
Now gather by degree, signs attached: squares, 3x^2 + x^2 = 4x^2; x terms, 2x - 5x = -3x. The sum is 4x^2 - 3x.
Every skill here is old: parentheses removal from Fundamentals, like-term collection from the last chapter. Polynomials are where those habits start paying compound interest.
Challenge
MediumAdd: 2x^2 + 4x + (3x^2 - x).
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 Negative9Adding and Subtracting
Adding PolynomialsSubtracting PolynomialsThe Minus Reaches EverythingPerimeter as a PolynomialRecap: Add and Subtract