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Worksheet: Writing and Evaluating Polynomial Expressions

In this worksheet, we will practice solving word problems through forming and evaluating polynomial expressions using the information provided in the questions.

Q1:

Write, in the simplest form, an expression that represents the perimeter of the given triangle.

  • A 1 1 π‘₯ + 6
  • B 1 6 π‘₯ βˆ’ 6
  • C 1 1 π‘₯ βˆ’ 6
  • D 1 6 π‘₯ + 6
  • E 1 6 π‘₯ + 1 0

Q2:

The figure below shows a rectangle whose length is 7 cm and width is π‘Ž cm. If its perimeter is 𝑝 cm, write a formula for 𝑝 in terms of π‘Ž and find the perimeter when π‘Ž is 4 cm.

  • A 𝑝 = 2 ( 7 + π‘Ž ) , 11 cm
  • B 𝑝 = 7 + π‘Ž , 22 cm
  • C 𝑝 = 2 ( 7 + π‘Ž ) , 28 cm
  • D 𝑝 = 2 ( 7 + π‘Ž ) , 22 cm

Q3:

The figure below shows a rectangle whose length is 3 cm and width is π‘Ž cm. If its perimeter is 𝑝 cm, write a formula for 𝑝 in terms of π‘Ž and find the perimeter when π‘Ž is 2 cm.

  • A 𝑝 = 2 ( 3 + π‘Ž ) , 5 cm
  • B 𝑝 = 3 + π‘Ž , 10 cm
  • C 𝑝 = 2 ( 3 + π‘Ž ) , 6 cm
  • D 𝑝 = 2 ( 3 + π‘Ž ) , 10 cm

Q4:

Find an expression for the area of the shaded region in the figure below.

  • A 8 2 π‘₯ 2
  • B 7 4 π‘₯
  • C 8 2 π‘₯
  • D 7 4 π‘₯ 2
  • E 7 8 π‘₯ 2

Q5:

Write an expression for the total area of the rectangle.

  • A ( 1 0 π‘₯ + 9 𝑦 ) square units
  • B ( 2 0 π‘₯ + 1 8 𝑦 ) square units
  • C 9 0 π‘₯ 𝑦 3 3 square units
  • D 9 0 π‘₯ 𝑦 square units

Q6:

Write an expression for the total area of the rectangle.

  • A ( 1 6 π‘₯ + 2 7 𝑦 ) square units
  • B ( 3 2 π‘₯ + 5 4 𝑦 ) square units
  • C 4 3 2 π‘₯ 𝑦 3 3 square units
  • D 4 3 2 π‘₯ 𝑦 square units

Q7:

Write an expression for the area of the shaded region in the shape below.

  • A 1 2 5 𝑀 + 1 7 5 𝑀 2
  • B 1 5 2 𝑀 + 1 6 3 𝑀 2
  • C 1 3 1 𝑀 + 2 0 𝑀 2
  • D 1 2 5 𝑀 + 1 6 3 𝑀 2

Q8:

What is the total shaded area in the figure below?

  • A 6 4 π‘Ž 𝑏 + 8 3 𝑏
  • B 6 5 π‘Ž 𝑏 + 8 3 𝑏
  • C 6 5 π‘Ž 𝑏 + 8 2 𝑏
  • D 6 3 π‘Ž 𝑏 + 8 1 𝑏

Q9:

Find an expression for the area of the shape shown below.

  • A 4 7 π‘₯ 2
  • B 2 8 π‘₯ 2
  • C 4 5 π‘₯ 2
  • D 4 3 π‘₯ 2
  • E 4 4 π‘₯ 2

Q10:

Sophia received $75 on her birthday to buy a gift. She bought three new pairs of pants for 𝑠 dollars each. Write an expression to represent the amount of money she has left. Given that each pair costs $21, how much money does she have left?

  • A 3 𝑠 , $63
  • B 7 5 βˆ’ 𝑠 , $54
  • C 7 5 + 3 𝑠 , $138
  • D 7 5 βˆ’ 3 𝑠 , $12
  • E 7 5 βˆ’ 2 1 𝑠 , $12

Q11:

Sophia received $90 on her birthday to buy a gift. She bought three new pairs of pants for 𝑠 dollars each. Write an expression to represent the amount of money she has left. Given that each pair costs $16, how much money does she have left?

  • A 3 𝑠 , $48
  • B 9 0 βˆ’ 𝑠 , $74
  • C 9 0 + 3 𝑠 , $138
  • D 9 0 βˆ’ 3 𝑠 , $42
  • E 9 0 βˆ’ 1 6 𝑠 , $42

Q12:

An online art store sells paint brushes for $12 each and oil colors for $10 each and charges $7.5 per order for shipping. Denoting the number paint brushes by 𝑝 and that of oil colors by 𝑐 , write an expression that represents the total cost, and then calculate the cost of one order of 7 brushes and 9 oil colors.

  • A ( 7 Γ— 𝑝 ) + ( 9 Γ— 𝑐 ) + 7 . 5 , $181.5
  • B ( 1 2 Γ— 𝑝 ) + ( 1 0 Γ— 𝑐 ) , $174
  • C ( 1 9 . 5 Γ— 𝑝 ) + ( 1 7 . 5 Γ— 𝑐 ) , $294
  • D ( 1 2 Γ— 𝑝 ) + ( 1 0 Γ— 𝑐 ) + 7 . 5 , $181.5
  • E ( 1 4 . 5 Γ— 𝑝 ) + ( 1 6 . 5 Γ— 𝑐 ) , $339

Q13:

An online art store sells paint brushes for $13 each and oil colors for $10 each and charges $8.5 per order for shipping. Denoting the number paint brushes by 𝑝 and that of oil colors by 𝑐 , write an expression that represents the total cost, and then calculate the cost of one order of 8 brushes and 5 oil colors.

  • A ( 8 Γ— 𝑝 ) + ( 5 Γ— 𝑐 ) + 8 . 5 , $162.5
  • B ( 1 3 Γ— 𝑝 ) + ( 1 0 Γ— 𝑐 ) , $154
  • C ( 2 1 . 5 Γ— 𝑝 ) + ( 1 8 . 5 Γ— 𝑐 ) , $264.5
  • D ( 1 3 Γ— 𝑝 ) + ( 1 0 Γ— 𝑐 ) + 8 . 5 , $162.5
  • E ( 1 6 . 5 Γ— 𝑝 ) + ( 1 3 . 5 Γ— 𝑐 ) , $349.5

Q14:

Knowing that a year consists of 52 weeks, make a table to find the algebraic expression that relates the number of weeks to the number of years 𝑛 . If the Greens have been living in a neighborhood for 19 years, determine that duration in weeks.

  • A 5 2 ( 𝑛 βˆ’ 1 ) , 936 weeks
  • B 5 2 + 𝑛 , 71 weeks
  • C 5 2 + ( 𝑛 βˆ’ 1 ) , 70 weeks
  • D 5 2 𝑛 , 988 weeks
  • E 5 2 ( 𝑛 + 1 ) , 1 040 weeks

Q15:

A farmer harvested 36 pounds of cotton this year. Given that there are 16 ounces in 1 pound, determine, by making a table, the algebraic expression that relates the number of ounces to that of pounds, and find how many ounces of cotton the farmer harvested.

  • A 1 6 ( 𝑛 βˆ’ 1 ) , 560 oz
  • B 1 6 + 𝑛 , 52 oz
  • C 1 6 + 𝑛 , 51 oz
  • D 1 6 𝑛 , 576 oz
  • E 1 6 ( 𝑛 + 1 ) , 592 oz

Q16:

Write an expression for the product of the cube of π‘₯ and the difference between 𝑦 and 7, all decreased by 2.

  • A 2 π‘₯ ( 𝑦 βˆ’ 7 ) 3
  • B π‘₯ ( 𝑦 βˆ’ 7 ) 3
  • C π‘₯ 𝑦 βˆ’ 9 3
  • D π‘₯ ( 𝑦 βˆ’ 7 ) βˆ’ 2 3
  • E π‘₯ ( 𝑦 βˆ’ 7 ) 2 3

Q17:

Express the following as an algebraic expression: the difference between a number 𝑝 and 0.6, decreased by the same number 𝑝 raised to the fifth power.

  • A 𝑝 + 0 . 6 + 𝑝 5
  • B 𝑝 + 0 . 6 βˆ’ 𝑝 5
  • C 𝑝 βˆ’ 0 . 6 + 𝑝 5
  • D 𝑝 βˆ’ 0 . 6 βˆ’ 𝑝 5
  • E 𝑝 + 0 . 6 βˆ’ 𝑝 5

Q18:

Write an expression for the cube of a number 𝑦 .

  • A 3 𝑦 3
  • B 3 𝑦
  • C 𝑦 3
  • D 𝑦 3
  • E 3 + 𝑦

Q19:

Write an expression for the area in cm2 of a triangle of height 1 0 π‘₯ cm and base 1 0 π‘₯ 3 cm.

  • A 5 0 π‘₯ cm2
  • B 1 0 0 π‘₯ 4 cm2
  • C 5 0 π‘₯ 3 cm2
  • D 5 0 π‘₯ 4 cm2
  • E 1 0 π‘₯ 4 cm2

Q20:

A square has sides of length 𝑙 . A new square is formed with double the side length. Find the perimeter 𝑃 and area 𝐴 of this new square.

  • A 𝑃 = 2 𝑙 , 𝐴 = 𝑙 2
  • B 𝑃 = 4 𝑙 , 𝐴 = 2 𝑙 2
  • C 𝑃 = 6 𝑙 , 𝐴 = 8 𝑙 2
  • D 𝑃 = 8 𝑙 , 𝐴 = 4 𝑙 2
  • E 𝑃 = 1 6 𝑙 , 𝐴 = 1 6 𝑙 2

Q21:

Find an expression for the perimeter of the shape shown below.

  • A 3 2 π‘₯
  • B 3 1 π‘₯
  • C 3 3 π‘₯
  • D 3 8 π‘₯
  • E 2 1 π‘₯

Q22:

What is the perimeter of a square whose side length is 4 0 π‘₯ cm?

  • A ( 1 6 0 βˆ’ π‘₯ ) cm
  • B ( 1 6 0 + π‘₯ ) cm
  • C ( 1 6 0 Γ· π‘₯ ) cm
  • D 1 6 0 π‘₯ cm

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