Worksheet: 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:

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

  • A 8 2 ๐‘ฅ ๏Šจ
  • B 7 4 ๐‘ฅ
  • C 8 2 ๐‘ฅ
  • D 7 4 ๐‘ฅ ๏Šจ
  • E 7 8 ๐‘ฅ ๏Šจ

Q2:

Express the perimeter of the figure below in terms of ๐‘ฅ .

  • A 5 0 ๐‘ฅ ๏Šจ length units
  • B 3 3 ๐‘ฅ length units
  • C 4 9 ๐‘ฅ ๏Šจ length units
  • D 6 6 ๐‘ฅ length units
  • E 2 7 2 ๐‘ฅ length units

Q3:

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

  • A 1 1 ๐‘ฅ + 6
  • B 1 6 ๐‘ฅ โˆ’ 6
  • C 1 1 ๐‘ฅ โˆ’ 6
  • D 1 6 ๐‘ฅ + 6
  • E 1 6 ๐‘ฅ + 1 0

Q4:

The figure below shows a rectangle whose length is 7 cm and width is ๐‘Ž cm. If its perimeter is ๐‘ cm, write a formula for ๐‘ in terms of ๐‘Ž and find the perimeter when ๐‘Ž is 4 cm.

  • A ๐‘ = 2 ( 7 + ๐‘Ž ) , 11 cm
  • B ๐‘ = 7 + ๐‘Ž , 22 cm
  • C ๐‘ = 2 ( 7 + ๐‘Ž ) , 28 cm
  • D ๐‘ = 2 ( 7 + ๐‘Ž ) , 22 cm

Q5:

Write an expression for the total area of the rectangle.

  • A ( 1 0 ๐‘ฅ + 9 ๐‘ฆ ) square units
  • B ( 2 0 ๐‘ฅ + 1 8 ๐‘ฆ ) square units
  • C 9 0 ๐‘ฅ ๐‘ฆ ๏Šฉ ๏Šฉ square units
  • D 9 0 ๐‘ฅ ๐‘ฆ square units

Q6:

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

  • A 1 2 5 ๐‘ค + 1 7 5 ๐‘ค 2
  • B 1 5 2 ๐‘ค + 1 6 3 ๐‘ค 2
  • C 1 3 1 ๐‘ค + 2 0 ๐‘ค 2
  • D 1 2 5 ๐‘ค + 1 6 3 ๐‘ค 2

Q7:

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

  • A 4 7 ๐‘ฅ ๏Šจ
  • B 2 8 ๐‘ฅ ๏Šจ
  • C 4 5 ๐‘ฅ ๏Šจ
  • D 4 3 ๐‘ฅ ๏Šจ
  • E 4 4 ๐‘ฅ ๏Šจ

Q8:

What is the total shaded area in the figure below?

  • A 6 4 ๐‘Ž ๐‘ + 8 3 ๐‘
  • B 6 5 ๐‘Ž ๐‘ + 8 3 ๐‘
  • C 6 5 ๐‘Ž ๐‘ + 8 2 ๐‘
  • D 6 3 ๐‘Ž ๐‘ + 8 1 ๐‘

Q9:

Amira received $75 on her birthday to buy a gift. She bought three new pairs of pants for ๐‘  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 ๐‘  , $63
  • B 7 5 โˆ’ ๐‘  , $54
  • C 7 5 + 3 ๐‘  , $138
  • D 7 5 โˆ’ 3 ๐‘  , $12
  • E 7 5 โˆ’ 2 1 ๐‘  , $12

Q10:

An online art shop sells paint brushes for $12 each and oil colours for $10 each and charges $7.5 per order for shipping. Denoting the number paint brushes by ๐‘ and that of oil colours by ๐‘ , write an expression that represents the total cost, and then calculate the cost of one order of 7 brushes and 9 oil colours.

  • A ( 7 ร— ๐‘ ) + ( 9 ร— ๐‘ ) + 7 . 5 , $181.5
  • B ( 1 2 ร— ๐‘ ) + ( 1 0 ร— ๐‘ ) , $174
  • C ( 1 9 . 5 ร— ๐‘ ) + ( 1 7 . 5 ร— ๐‘ ) , $294
  • D ( 1 2 ร— ๐‘ ) + ( 1 0 ร— ๐‘ ) + 7 . 5 , $181.5
  • E ( 1 4 . 5 ร— ๐‘ ) + ( 1 6 . 5 ร— ๐‘ ) , $339

Q11:

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 ๐‘› . If the Greens have been living in a neighborhood for 19 years, determine that duration in weeks.

  • A 5 2 ( ๐‘› โˆ’ 1 ) , 936 weeks
  • B 5 2 + ๐‘› , 71 weeks
  • C 5 2 + ( ๐‘› โˆ’ 1 ) , 70 weeks
  • D 5 2 ๐‘› , 988 weeks
  • E 5 2 ( ๐‘› + 1 ) , 1,040 weeks

Q12:

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 ( ๐‘› โˆ’ 1 ) , 560 oz
  • B 1 6 + ๐‘› , 52 oz
  • C 1 6 + ๐‘› , 51 oz
  • D 1 6 ๐‘› , 576 oz
  • E 1 6 ( ๐‘› + 1 ) , 592 oz

Q13:

Write an expression for the product of the cube of ๐‘ฅ and the difference between ๐‘ฆ and 7, all decreased by 2.

  • A 2 ๐‘ฅ ( ๐‘ฆ โˆ’ 7 ) 3
  • B ๐‘ฅ ( ๐‘ฆ โˆ’ 7 ) 3
  • C ๐‘ฅ ๐‘ฆ โˆ’ 9 3
  • D ๐‘ฅ ( ๐‘ฆ โˆ’ 7 ) โˆ’ 2 3
  • E ๐‘ฅ ( ๐‘ฆ โˆ’ 7 ) 2 3

Q14:

Express the following as an algebraic expression: the difference between a number ๐‘ and 0.6, decreased by the same number ๐‘ raised to the fifth power.

  • A ๐‘ + 0 . 6 + ๐‘ 5
  • B ๐‘ + 0 . 6 โˆ’ ๐‘ 5
  • C ๐‘ โˆ’ 0 . 6 + ๐‘ 5
  • D ๐‘ โˆ’ 0 . 6 โˆ’ ๐‘ 5
  • E ๐‘ + 0 . 6 โˆ’ ๐‘ 5

Q15:

Write an expression for the cube of a number ๐‘ฆ .

  • A 3 ๐‘ฆ 3
  • B 3 ๐‘ฆ
  • C ๐‘ฆ 3
  • D ๐‘ฆ 3
  • E 3 + ๐‘ฆ

Q16:

Write an expression for the area in cm2 of a triangle of height 1 0 ๐‘ฅ cm and base 1 0 ๐‘ฅ ๏Šฉ cm.

  • A 5 0 ๐‘ฅ cm2
  • B 1 0 0 ๐‘ฅ ๏Šช cm2
  • C 5 0 ๐‘ฅ ๏Šฉ cm2
  • D 5 0 ๐‘ฅ ๏Šช cm2
  • E 1 0 ๐‘ฅ ๏Šช cm2

Q17:

A square has sides of length ๐‘™ . A new square is formed with double the side length. Find the perimeter ๐‘ƒ and area ๐ด of this new square.

  • A ๐‘ƒ = 2 ๐‘™ , ๐ด = ๐‘™ 2
  • B ๐‘ƒ = 4 ๐‘™ , ๐ด = 2 ๐‘™ 2
  • C ๐‘ƒ = 6 ๐‘™ , ๐ด = 8 ๐‘™ 2
  • D ๐‘ƒ = 8 ๐‘™ , ๐ด = 4 ๐‘™ 2
  • E ๐‘ƒ = 1 6 ๐‘™ , ๐ด = 1 6 ๐‘™ 2

Q18:

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

  • A 3 2 ๐‘ฅ
  • B 3 1 ๐‘ฅ
  • C 3 3 ๐‘ฅ
  • D 3 8 ๐‘ฅ
  • E 2 1 ๐‘ฅ

Q19:

What is the perimeter of a square whose side length is 4 0 ๐‘ฅ cm?

  • A ( 1 6 0 โˆ’ ๐‘ฅ ) cm
  • B ( 1 6 0 + ๐‘ฅ ) cm
  • C ( 1 6 0 รท ๐‘ฅ ) cm
  • D 1 6 0 ๐‘ฅ cm

Q20:

The figure below shows a rectangle whose length is 3 cm and width is ๐‘Ž cm. If its perimeter is ๐‘ cm, write a formula for ๐‘ in terms of ๐‘Ž and find the perimeter when ๐‘Ž is 2 cm.

  • A ๐‘ = 2 ( 3 + ๐‘Ž ) , 5 cm
  • B ๐‘ = 3 + ๐‘Ž , 10 cm
  • C ๐‘ = 2 ( 3 + ๐‘Ž ) , 6 cm
  • D ๐‘ = 2 ( 3 + ๐‘Ž ) , 10 cm

Q21:

Write an expression for the total area of the rectangle.

  • A ( 1 6 ๐‘ฅ + 2 7 ๐‘ฆ ) square units
  • B ( 3 2 ๐‘ฅ + 5 4 ๐‘ฆ ) square units
  • C 4 3 2 ๐‘ฅ ๐‘ฆ ๏Šฉ ๏Šฉ square units
  • D 4 3 2 ๐‘ฅ ๐‘ฆ square units

Q22:

Amira received $90 on her birthday to buy a gift. She bought three new pairs of pants for ๐‘  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 ๐‘  , $48
  • B 9 0 โˆ’ ๐‘  , $74
  • C 9 0 + 3 ๐‘  , $138
  • D 9 0 โˆ’ 3 ๐‘  , $42
  • E 9 0 โˆ’ 1 6 ๐‘  , $42

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