4.4 Problem Solving with Polynomials

Practice 1

a) Write an expression in the form ax2 + bx + c to represent the area of the given figure.
b) Calculate the area if x = 1.5.

Upside down L shaped figure. Top side is 2x+6. Left side is 3x+3. Bottom left side is x. Top right side is x+1. Two sides missing.

 

 

 

 

 

 

 
Practice 2

a) Write an expression in the form ax2 + bx + c to represent the area of the shaded portion of the figure.
b) Determine the area of the shaded portion given that x = 15.

Larger grey rectangle with dimensions 3x and 6x+1. Smaller white rectangle inside of larger grey rectangle with dimensions 2x+5 and 3x+5.

 

 

 

 

 

 

 

 
Practice 3

a) A backyard is the shape of a triangle and has a base of (x – 5) m and a height of (4x – 4) m. Write an expression to represent the area of the backyard in the form ax2 + bx + c.
b) Find the area of the backyard given that x = 10.

 

 

 

 
Practice 4

a) Write an expression in the form ax2 + bx + c in terms of pi (π) to represent the area of the circle.
b) If x = 0.7, what is the area of the circle? Round to the nearest tenth.

Circle with radius of x+4.

 

 

 

 

 

 

 
Practice 5

a) A rectangular prism has dimensions (x + 2) cm, (3x) cm, and (3x – 1) cm. Write an expression in the form ax3 + bx2 + cx to represent the volume of the figure.
b) Determine the volume of the figure if x = 4.

 

 

 

 

 
Practice 6

A square with side lengths (x + 1) ft and a rectangle with side lengths (x – 3) ft and (x + 7) ft have equal areas. Determine the value of x.

 

 

 

 

 

Homework

  1. a) Write an expression in the form ax2 + bx + c to represent the area of the given figure.
    b) Calculate the area if x = 2.3.

    Upside down L shaped figure. Top side is 7x-2. Left side is 4x+2. Bottom right side is 3x-2. Bottom right side is 4x+1. Two sides missing.

     

     
  2. a) Write an expression in the form ax2 + bx + c to represent the area of the shaded portion of the figure.
    b) Determine the area of the shaded portion if x = 9.

    Larger grey rectangle with dimensions 2x+8 and 4x-4. Smaller white square inside of larger grey rectangle with side lengths x+5.

     
  3. a) Write an expression in the form ax2 + bx + c to represent the area of the triangle.
    b) Determine the area of the shaded portion if x = 2.2.

    Right triangle with a base of 2x+6 and height of x+2.

     
  4. a) Write an expression in the form ax2 + bx + c to represent the area in terms of pi (π) of a circle with a diameter of 2x – 8.
    b) Find the area of the circle if x = 0.7. Round to the nearest hundredth.

     

     

     

     

     

     
  5. a) Write an expression in the form as3 + bs2 + cs + d to represent the volume of the figure below.
    b) If s = 3, what is the volume of the figure?

    Rectangular prism with side lengths s, s, and s-1.

     

  6. A triangle has a base of (3p – 2) mm and a height of (2p + 1) mm. A rectangle with side lengths (3p + 4) mm and (p – 2) mm has the same area as the triangle. Determine the value of p.

     

     

     

     

     

     

  7. A square with side lengths (2x – 1) in and a rectangle with side lengths (2x + 1) in and (2x – 1) in have equal areas. Determine the value of x.

     

     

     

     

     

     
  8. a) Write an expression to represent the area of a triangle with a height of (3a + 4) and a base of (8a – 2).
    b) If a rectangle with side lengths (3a – 1) km and (4a – 1) km has the same area as the triangle, find the value of a. Leave your answer as an exact value.

     

     

     

     

     

Answers

1. a) 16x2 + 11x – 2
b) 107.94		 2. a) 7x2 + 20x – 36
b) 711		 3. a) x2 + 5x + 6
b) 21.84		 4. a) πx2 – 8πx + 16π
b) 34.21
5. a) s3 – s2
b) 18		 6. \frac{-14}{3} 7. \frac{1}{2} 8. a) 12a2 + 13a – 4
b) \frac{1}{4}

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