Question

solve by adding the polynomials. the models needed for the situation are provided.1. a farmer must add the areas of two plots of land to determine the amount of seed to plant. the area of plot a can be represented by $3x^2 + 7x - 5$, and the area of plot b can be represented by $5x^2 - 4x + 11$. write a polynomial that represents the total area of both plots of land.explain 3b modeling with polynomials□ read the section below and complete the following activity (adapted from lesson 17.2).as seen in the previous example, polynomials can be used to model rectangles. sometimes before adding polynomials, you may need to consider the relationship between the polynomials. when working with perimeter problems, recall that the perimeter is the sum of all side lengths. therefore, to find the perimeter, you must add the length twice and the width twice.examples model the situation with the sum of polynomials. simplify their sum.a. rebecca is building a rectangular pen for her rabbits. the polynomial $4n + 8$ represents the length of the rabbit pen and the polynomial $2n + 6$ represents the width of the rabbit pen. write a polynomial that represents the perimeter of the rabbit pen.$(2n + 6) + (2n + 6) + (4n + 8) + (4n + 8)$ use plus (+) signs to add the polynomials.$2n + 6 + 2n + 6 + 4n + 8 + 4n + 8$ remove the parenthesis.$(2n + 2n + 4n + 4n) + (6 + 6 + 8 + 8)$ rearrange terms so that like terms are together.$12n + 28$ combine like terms.the perimeter of the rabbit pen is modeled by the polynomial $12n + 28$.model the situation with the sum of polynomials. simplify their sum.1. a rectangular picture frame has the dimensions shown in the figure. write a polynomial that represents the perimeter of the frame.$3x + 1$$5x - 2$

Explanation:

Step1: Set up perimeter sum

$(3x+1)+(3x+1)+(5x-2)+(5x-2)$

Step2: Remove parentheses

$3x+1+3x+1+5x-2+5x-2$

Step3: Group like terms

$(3x+3x+5x+5x)+(1+1-2-2)$

Step4: Combine like terms

$16x - 2$

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Step1: Set up total area sum

$(3x^2+7x-5)+(5x^2-4x+11)$

Step2: Remove parentheses

$3x^2+7x-5+5x^2-4x+11$

Step3: Group like terms

$(3x^2+5x^2)+(7x-4x)+(-5+11)$

Step4: Combine like terms

$8x^2 + 3x + 6$

Answer:

1. Total land area: $8x^2 + 3x + 6$
2. Picture frame perimeter: $16x - 2$