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Solving these problems involves the use of polynomials. Students should be able to multiply, add and subtract polynomial expressions.

Problems which deal more specifically with quadratics can be found in the Quadratics category.

Some of these problems are also in the following subcategories:

Related Resources
Interactive resources from our Math Tools project:
   Algebra: Polynomials
The closest match in our Ask Dr. Math archives:
   High School: Polynomials
NCTM Standards:
   Algebra Standard for Grades 9-12

Access to these problems requires a Membership.

Alvin's Theorem - Terry Trotter
Algebra, difficulty level 2. Alvin notices that the difference between any two consecutive square numbers can also be expressed as the sum of consecutive integers. Can you use algebra to show that this pattern is always true? ... more>>

Are You Ready for Some Football? - Steve Risberg
Algebra, difficulty level 2. The Algenauts football team racked up 229 yards rushing in their first game. Given descriptions of how many yards each of the players ran for in relation to each other, determine the exact yardage each one had. ... more>>

Baffling Brother - Steve Risberg
Algebra, difficulty level 2. Brandon wows his sister by having her choose a secret number and make a series of calculations, then telling her what her final answer is. Can you use variables and algebra to explain how Brandon did it? ... more>>

Calendar Calculations - Steve Risberg
Algebra, difficulty level 1. Write variable expressions for dates in a calendar pattern and use your expressions to explore a numeric relationship among those dates. ... more>>

Count Your Change - Steve Risberg & Terry Trotter
Algebra, difficulty level 3. I have three times as many nickels as dimes in my pocket. If the number of coins is reversed, by what percent will the value of the money in my pocket increase? ... more>>

Examining an Equation - Steve Risberg
Algebra, difficulty level 2. Find integer solutions to an equation in two variables. ... more>>

An Expanding Circle - Steve Risberg
Algebra, difficulty level 2. When the radius of a circle increases by 6 inches, the area increases by 125%. Find the original radius. ... more>>

Factor Bingo - Steve Risberg
Algebra, difficulty level 1. You're playing Factor Bingo. Determine what squares on your card you can cover so far and create a polynomial that will let you win on the next turn. ... more>>

Flying Off the Shelves - Steve Risberg
Algebra, difficulty level 1. The new soundtrack album from the movie Ray is selling like hotcakes! Given some information about the sales over three days at Tip Top Tunes, can you determine how many CDs sold per day? ... more>>

Mr. Fachtore's Gardens - Steve Risberg
Algebra, difficulty level 1. Mr. Fachtore has decided to plant two gardens this year - one rectangular and one square. Given algebraic expressions for the areas of the gardens, find algebraic expressions for their dimensions. ... more>>

Polynomial Power - Steve Risberg
Algebra, difficulty level 3. Given the value of one variable expression, can you use it to find the value of others? ... more>>

Polynomial Puzzler - Steve Risberg
Algebra, difficulty level 2. Given four polynomials, find an expression that uses each of them once, involves multiplication, addition and subtraction, and results in a given binomial when simplified. ... more>>

A Product-Plus-1 - Terry Trotter
Algebra, difficulty level 3. The product of any four consecutive integers, increased by one, is always a square number. Give at least three instances of that statement and prove that this will always occur by finding an algebraic expression for that "square number." ... more>>

September Squares - Cynthia Lanius and Steve Risberg
Algebra, difficulty level 2. Use a variable to explain how you can be given the sum of four dates that form a block on a calendar and determine what the four dates must be. ... more>>

Swapping Marbles - Lillian Ray, Steve Risberg, and Steve Weimar
Algebra, difficulty level 3. Three kids swap marbles in an interesting way. After the swapping, which of the three had gained the most marbles? How many did they gain? ... more>>

The Great Northern Triathlon - Steve Risberg
Algebra, difficulty level 2. Sven skis, skates, and snowshoes in the winter triathlon. Use the given information to determine how fast he snowshoes. ... more>>

Three Consecutive Integers - Annie Fetter
Algebra, difficulty level 1. Use a variable to explain an interesting relationship that can be found between three consecutive integers. ... more>>

To B or Not To B - Steve Risberg
Algebra, difficulty level 2. Given a letter pattern, find expressions for the number of B's and the ratio of B's to total letters in the nth term. ... more>>

Trick-or-Treat Box - Terry Trotter
Algebra, difficulty level 1. Harvey and his classmates make trick-or-treat boxes in math class and use a special formula to find the volumes. ... more>>

Wreck Tangle - Steve Risberg
Algebra, difficulty level 2. When the width of a given rectangle is tripled and the length is doubled, the perimeter increases by 92 cm. Find the area of the original rectangle. ... more>>

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