Polynomial Lab          Name:  ________________________

 

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Find the length and width of the rectangle below:

 

John has a bad memory so he only wanted to remember 1 number to figure out the length and width of his pool.  The problem was he forgot the number but remember that the length was two times the number plus two and the width was the number reduced by 5.

John is going to have a pool party and wants to put lights around his pool.  The lights are 84 feet long. (Perimeter is 84 feet).  Help John find out the number and the length and width of his pool. 

 

                                                                     

 

                          


 

                                                      

 

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Find the expression to find the perimeter of the triangle

 

 

                                                                                                                                                                                                                                                             

 

                       

 

                                                                                         

                        

 

 

 

                                                                                

 

 

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If x equals 2 what is the perimeter of the triangle.

 

A)    Substitute x = 2 into the polynomial of each side then add up the sides.

 

 

 

 

B)     Substitute x = 2 into the polynomial expression of the perimeter to find the perimeter.

 

 

 

 

C)    Do your answers match?

Find the expression to find the area of the rectangle:

(Area of a rectangle is length times width)

 

 

 

                                                                           x + 15

 

 

       

 

 

 

 

 

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If x equals 3 what is the area of the rectangle.

 

D)    Substitute x = 3 into the polynomial of each side then multiple the sides.

 

 

 

 

E)     Substitute x = 3 into the polynomial expression of the area to find the area.

 

 

 

 

F)     Do your answers match?

 

Find the expression to find the volume of the rectangle below:

(Volume of a rectangle is length times width times height.)

 

                                            

                                                                                                                                                                                                                                                                 

                                                               

                                                                                                                                                 

                                                     

                                                            x - 3

                                           

 

                              x + 3 

 

                                                                                                    

 

 

 

 

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If x equals 4 what is the area of the rectangle.

 

G)    Substitute x = 4 into the polynomial of each side then multiple the sides.

 

 

 

 

H)    Substitute x = 4 into the polynomial expression of the area to find the area.

 

 

 

 

I)       Do your answers match?

 

 

 

 

 

SOLUTIONS TO POLYNOMIAL LAB

 

Find the length and width of the rectangle below:

 

John has a bad memory so he only wanted to remember 1 number to figure out the length and width of his pool.  The problem was he forgot the number but remember that the length was two times the number plus two and the width was the number reduced by 5.

Help John find out the number and the length and width of his pool.  John is going to have a pool party and wants to put lights around his pool.  The lights are 84 feet long. (Perimeter is 84 feet).  Find the length and width of the pool.

 

 

                                                                     

 

                           


 

                                                      

 

(2x + 2) + (x – 5) + (2x + 2) + (x – 5) = 84

 

2x + 2 + x – 5 + 2x + 2 + x – 5 = 84

 

Combine like terms:      2x + x + 2x + x = 6x

                                    2 + 2 - 5 – 5                  = -6

 

6x – 10 = 80

 

Solve for x:       6x         – 6      =          84

                                     + 6                 +6   

                        6x                    =          90

                        6                                  6

 

                        x                      =          15

 

Length = 2x + 2 = 2(15) + 2 = 32 Feet

Width  =  x – 5  = (15) – 5   = 10 Feet

 

Check:  32 + 10 + 32 + 10 =  84 Feet

 

 

 

Find the expression to find the perimeter of the triangle

 

 

                                                                                                                                                                                                                                                             

 

                       

 

                                                                                                    

                        

 

 

 

                                                                                 

 

Answer:

 

++=

 

 

Combine like terms:

 

 

-5x – 2x + 3x = -4x

 

7– 4 – 5 = -2

 

Answer:

 

If x equals 2 what is the perimeter of the triangle.

 

A)    Substitute x = 2 into the polynomial of each side then add up the sides

++=

9+ 16 + 9 = 34

B)     Substitute x = 2 into the polynomial expression of the perimeter to find the perimeter.

=

44    - 8 – 2 = 34

C)    Do your answers match?  YES

 

Find the expression to find the area of the rectangle:

(Area of a rectangle is length times width)

 

 

 

                                                                           x + 15

 

 

           

 

 


 

Answer:

Multiple the polynomials:

 

(x + 15)()=

 

Distributive the terms:

 

 

Combine Like Terms:

 

 

Another Method:  Table Method

 

 

-3x

2

x

2x

15

-45x

30

Rewrite:

 

 

Combine Like Terms:

 

 

 

If x equals 3 what is the area of the rectangle.

 

D)    Substitute x = 3 into the polynomial of each side then add up the sides

 

()(3+ 15)=

 

(11)(18)=  198

 

 

 

E)     Substitute x = 3 into the polynomial expression of the area to find the area.

 

=

198

 

 

F)     Do your answers match? YES

 

 

 

 

Find the expression to find the volume of the rectangle below:

(Volume of a rectangle is length times width times height.)

 

 

                                                 

 

 

                                                                                                                                         

                                                                                                                                                                                                                                                 

                                                                   

                                                                                                                                                 

                                                     

                                                            x - 3

                                           

 

                              x + 3 

 

                                                                                                    

 

Answer:

 

()(x + 3)()=

 

Multiply the first two.  Use FOIL.

 

()(x + 3) =

 

Then multiple the product by the last side:

 

()()=

 

Combine Like Terms:

 

 

 

 

Another Method:  Table Method

 

 

-2

x

-2x

+3

3

-6


 

Rewrite equation:

 

 

 

 

-2x

-6

-3x

-

18x

 

Rewrite the equation:

 

 

Combine Like Terms:

 

 

 

If x equals 4 what is the area of the rectangle.

 

G)    Substitute x = 4 into the polynomial of each side then multiple the sides

(4 + 3)()(=

(7)(14)(20)= 1960

 

 

 

H)    Substitute x = 4 into the polynomial expression of the area to find the area.

=

1960

 

      I)  Do your answers match?  YES