Chapter 8.1, Problem 1MP

(a)

To determine

To fill the blank space:

The polynomial that represent the length of Kelly’s plot is _______

Answer to Problem 1MP

$x+6$

Explanation of Solution

Given Information:

  

Calculation:

The length of planning area of Kelly’s plot =xft

The length of surrounding border = $3+3=6$ ft

∴The polynomial that represent total length of Kelly’s plot = $x+6$

(b)

To determine

To fill the blank space:

The polynomial that represent the width of Kelly’s plot is _______

Answer to Problem 1MP

$x+2$

Explanation of Solution

Given Information:

  

Calculation:

The width of planning area of Kelly’s plot =xft

The width of surrounding border = $1+1=2$ ft

∴The polynomial that represent total width of Kelly’s plot = $x+2$

(c)

To determine

To fill the blank space:

Each of the polynomial in part (b) and (c) is an example of _______

Answer to Problem 1MP

binomial

Explanation of Solution

Given Information:

Length of Kelly’s plot is $x+6$

Width of Kelly’s plot is $x+2$

Formula Used:

A binomial is an expression with two terms.

Length and width of Kelly’s plot contains two terms. Therefore each expression is an example of binomial.

(d)

To determine

To fill the blank space:

The polynomial that represents the area of Roberto’s flower bed is______

Answer to Problem 1MP

$x^2$$$

Explanation of Solution

Given Information:

  

Formula Used:

Area of a rectangle of length l and width b is lb

Calculation:

Length of Roberto’s flower bed, l$=x$

Width of Roberto's flower bed, b$=x$

Area of Roberto's flower bed, A$=lb$

  $=x\cdot x$

Area of Roberto's flower bed, A$=x^2$

(e)

To determine

To fill the blank space:

The polynomial that represents the area of Roberto’s flower bed is an example of a______

Answer to Problem 1MP

monomial

Explanation of Solution

Given Information:

The polynomial that represents the area of Roberto’s flower bed is $x^2$

The area of Roberto’s flower bed is $x^2$ , which contains only one term.

Therefore it is an example of a monomial.

(f)

To determine

To fill the blank space:

The degree of the polynomial that represents the area of Roberto’s flower bed is______

Answer to Problem 1MP

2 $$

Explanation of Solution

Given Information:

The polynomial that represents the area of Roberto’s flower bed is $x^2$

The degree of the monomial is the sum of the exponents of all included variables.

The area of Roberto’s flower bed has only one variable x and has exponent 2.

∴The degree of the polynomial that represents the area of Roberto’s flower bed is 2