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Polynomials

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 912
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 ProductPlus1
 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>>

TrickorTreat Box
 Terry Trotter

Algebra, difficulty level 1. Harvey and his classmates make trickortreat 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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