Perimeter as a Polynomial
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 45 of 64.
Polynomials earn their keep describing quantities that depend on an unknown. A rectangle has width w; its length runs 3 units longer, w + 3. Its perimeter is two lengths plus two widths, whatever w turns out to be.
Write that sentence in symbols, exactly as Fundamentals translated words into equations: p = 2(w + 3) + 2w. The structure mirrors the story: two of the length package, plus two widths.
Tidied with this chapter's tools, 2w + 6 + 2w collects to 4w + 6: a formula ready to take any width. Model first, tidy second; the two skills are one workflow now.
Challenge
MediumA rectangle's width is w; its length is 5 units longer. Write an equation for its perimeter p, following the story's structure. Type it onto the canvas.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
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