Add polynomials to find perimeter

What you'll learn

Identify like terms within polynomial expressions representing the sides of geometric figures with 80% accuracy.
Apply the rules of addition to combine like terms in polynomials to find the perimeter of triangles, rectangles, and other polygons with at least 70% accuracy on a worksheet.
Solve for the perimeter of a given polygon, represented by polynomial side lengths, and express the answer as a simplified polynomial in standard form in at least 3 out of 4 problems.
Explain, in writing, the steps involved in adding polynomials to find the perimeter of a shape, using correct mathematical vocabulary, with a rubric score of at least 3 out of 4.

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1

Introduction & Learning Objectives

Learning Objectives Define perimeter in the context of polynomial side lengths. Identify and group like terms within polynomials that represent the sides of a shape. Write a polynomial expression representing the perimeter of a polygon. Add multiple polynomials to find a simplified expression for the perimeter. Apply the perimeter formula for specific shapes like rectangles (P = 2l + 2w) when side lengths are polynomials. Evaluate the perimeter for a given value of the variable. Solve for a missing side length given the perimeter and other side lengths as polynomials. Ever tried to plan a garden or frame a picture where the dimensions weren't fixed numbers? 🖼️ Let's explore how to calculate the border needed when the lengths are algebraic expressions! This tutor...

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Key Concepts & Vocabulary

TermDefinitionExample PolynomialAn algebraic expression consisting of one or more terms, where each term is a product of a constant (the coefficient) and one or more variables raised to non-negative integer powers.The expression 5x^2 - 3x + 7 is a polynomial with three terms. PerimeterThe total distance around the boundary of a closed two-dimensional figure. It is calculated by adding the lengths of all the sides together.A triangle with side lengths of 3 cm, 4 cm, and 5 cm has a perimeter of 3 + 4 + 5 = 12 cm. TermA single part of a polynomial, which can be a number, a variable, or a product of numbers and variables.In the polynomial 4y^2 + 2y - 1, the terms are 4y^2, 2y, and -1. Like TermsTerms that have the exact same variables raised to the exact same powers. Only the coefficients can...

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Core Formulas

General Perimeter Formula P = s_1 + s_2 + s_3 + ... + s_n The perimeter (P) of any polygon is the sum of the lengths of all its sides (s_1, s_2, etc.). To find the perimeter, you add all the expressions representing the side lengths. Rule for Combining Like Terms ax^n + bx^n = (a+b)x^n To add polynomials, identify terms with the same variable and exponent. Add their coefficients and keep the variable part the same. This is the fundamental step in simplifying the perimeter expression. Perimeter of a Rectangle Formula P = 2l + 2w For a rectangle with length (l) and width (w), the perimeter is twice the length plus twice the width. This is a shortcut for adding the four sides (l + w + l + w).

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Sample Practice Questions

Challenging

The perimeter of a rectangle is (12x^2 + 6x - 24). The length of the rectangle is twice its width. What polynomial represents the length?

A.2x^2 + x - 4

B.6x^2 + 3x - 12

C.3x^2 + 1.5x - 6

D.4x^2 + 2x - 8

Easy

What is the general method for finding the perimeter of a polygon whose side lengths are represented by polynomials?

A.Add the polynomials representing the lengths of all sides.

B.Multiply the polynomials representing the lengths of all sides.

C.Find the average of the polynomials by adding them and dividing by the number of sides.

D.Subtract the polynomial for the shortest side from the polynomial for the longest side.

Easy

Which of the following is a pair of 'like terms' that can be combined when adding polynomials to find a perimeter?

A.3x^2 and 2x

B.5y and 5

C.-4x^2 and 7x^2

D.6xy and 6x

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Frequently asked questions

What grade level is "Add polynomials to find perimeter"?

Add polynomials to find perimeter is a Grade 9 Mathematics lesson on ExcelOS.

What will I learn in Add polynomials to find perimeter?

You'll be able to: Identify like terms within polynomial expressions representing the sides of geometric figures with 80% accuracy; Apply the rules of addition to combine like terms in polynomials to find the perimeter of triangles, rectangles….

Is "Add polynomials to find perimeter" free to practice?

Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.

How many practice questions are included with Add polynomials to find perimeter?

This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.