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Chapter 7: Q36. (page 461)

Write a polynomial that represents the perimeter of the figure.

Short Answer

Expert verified

The polynomial8x4+6x2+15x+2 represents the perimeter of the given figure.

Step by step solution

01

Step 1. Define standard form of a polynomial.

The standard form of a polynomial means, writing the polynomial in descending powers of the variable.

02

Step 2. Define like and unlike terms.

In algebra, like terms are the terms that have the same variables and powers.

The unlike terms are two or more terms that are not like terms.

03

Step 3. Define the perimeter of a figure.

Perimeter of a figure is the sum of the lengths of all the sides of the figure.

04

Step 4. Calculate the perimeter of the given figure.

Simplify the given difference by combining the like terms.

Add the lengths of all sides of the given figure.

The perimeter is

5x2+4x+4x+3x3+x2+1+x+1+6x+8x4=5x2+4x+4x+3x3+x2+1+x+1+6x+8x4

Simplify by combining the like terms

5x2+4x+4x+3x3+x2+1+x+1+6x+8x4=8x4+5x2+x2+4x+4x+x+6x+1+1=8x4+6x2+15x+2

So the perimeter=8x4+6x2+15x+2

Therefore the polynomial8x4+6x2+15x+2represents the perimeter of the given figure.

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