WORKSHEET ON TYPES OF ALGEBRAIC EXPRESSIONS

Classify the following polynomials based on number of terms.

Problem 1 :

4y – 7z

Solution

Problem 2 :

y²

Solution

Problem 3 :

x + y - xy

Solution

Problem 4 :

100

Solution

Problem 5 :

ab – a - b

Solution

Problem 6 :

5 – 3t

Solution

Problem 7 :

4p²q – 4pq²

Solution

Problem 8 :

7mn

Solution

Problem 9 :

z² – 3z + 8

Solution

Problem 10 :

a² + b²

Solution

Problem 11 :

z² + z

Solution

Problem 12 :

1 + x + x²

Solution

Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial.

Problem 1 :

3x²yz² – 3xy²z + x²yz² + 7xy²z

Solution

Problem 2 :

x⁴ + 3x³y + 3x²y² – 3x³y – 3xy³ + y⁴ – 3x²y²

Solution

Problem 3 :

p³q²r + pq²r³ + 3p²qr² – 9p²qr²

Solution

Problem 4 :

2a + 2b + 2c – 2a – 2b – 2c – 2b + 2c + 2a

Solution

Problem 5 :

50x³ – 21x + 107 + 41x³ – x + 1 – 93 + 71x – 31x³

Solution

Problem 6 :

Answer the questions or identify the specified parts of the polynomial:

5x³ - 2x² + 14x + 7x² + 3x - 11

a. How many terms does this polynomial have? _______

b. Write the term that has a degree of 3. ________

c. What is the coefficient of this term with degree 3? _______

d. Which term is a constant term? _______

e. List a pair of like terms. ________ and ________

f. List another pair of like terms. ________ and ________

g. Rewrite the polynomial in simplified form by combining the like terms:

h. Evaluate this polynomial for = 2. _________

Solution

Problem 7 :

Answer the questions or identify the specified parts of the polynomial: 

2ab² + 3a² b - 6b - 2a² b + 3a - b

a. How many terms does this polynomial have? _______

b. Write the term(s) that have a degree of 1. ________________________

c. What are the coefficients of the term(s) with degree 1? _____________________

d. Which term is a constant term? _______

e. List a pair of like terms. ________ and ________

f. List another pair of like terms. ________ and ________

g. Rewrite the polynomial in simplified form by combining the like terms:

h. Evaluate this simplified polynomial for a = 4 and b = −1

Solution

Evaluate the algebraic expression for the given values.

Problem 1 :

7x + 8 when x = 2

Solution

Problem 2 :

5x − 4 when x = 6

Solution

Problem 3 :

x² when x = 12

Solution

Problem 4 :

4^x when x = 2

Solution

Problem 5 :

x² + 3x - 7 when x = 4

Solution

Problem 6 :

(x - y)² when x = 10 and y = 7

Solution

Problem 7 :

a² + b² when a = 3 and b = 8

Solution

Problem 8 :

r² - s² when r = 12 and s = 5

Solution

Problem 9 :

2L + 2W when L = 15 and W = 12

Solution

Problem 10 :

2x + 4y - 5 when x = 7 and y = 8

Solution

Problem 11 :

It takes approximately 770 peanuts to product one jar of peanut butter. The total number of peanuts n is represented by the function n = 770 p, where p is the number of jars of peanut butter purchased. 

a) Determine the appropriate input values.

b) Complete the function table.

Solution

Problem 12 :

A taxi charges $2.50 plus 0.75 per mile. The function y = 0.75 x + 2.50 represents the total cost y, of the taxi ride for any number of miles. If Adriana rode 10 miles in the taxi and Alonso rode 15 miles, how much more did Alonso spend on his taxi ride ?

Solution

Problem 13 :

An elephant weighs 200 pounds at birth and gains approximately 2 pounds per day. The function w = 2d + 200 represents the weight w of an elephant on a given day d during his first year. How much more does an elephant weigh on Day 60 than it does on Day 5 ?

Solution

Problem 14 :

A public swimming pool holds 250,000 gallons of water and is being drained at the rate of 200 gallons per minute. The function g = -200 m + 250000 represents how many gallons remain in the pool g, after any number of minutes m, how much more water after 5 minutes than 20 minutes ?

Solution