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Polynomials
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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
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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.
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Alvin's Theorem
- Terry Trotter
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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>>
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Are You Ready for Some Football?
- Steve Risberg
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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>>
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Baffling Brother
- Steve Risberg
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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>>
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Calendar Calculations
- Steve Risberg
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Write variable expressions for dates in a calendar pattern and use your expressions to explore a numeric relationship among those dates.
... more>>
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Count Your Change
- Steve Risberg & Terry Trotter
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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>>
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An Expanding Circle
- Steve Risberg
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Algebra, difficulty level 2. When the radius of a circle increases by 6 inches, the area increases
by 125%. Find the original radius.
... more>>
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Flying Off the Shelves
- Steve Risberg
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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>>
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Mr. Fachtore's Gardens
- Steve Risberg
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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>>
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Polynomial Puzzler
- Steve Risberg
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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>>
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A Product-Plus-1
- Terry Trotter
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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>>
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September Squares
- Cynthia Lanius and Steve Risberg
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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>>
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Three Consecutive Integers
- Annie Fetter
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Algebra, difficulty level 1. Use a variable to explain an interesting relationship that can be found between three consecutive integers.
... more>>
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Trick-or-Treat Box
- Terry Trotter
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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>>
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Wreck Tangle
- Steve Risberg
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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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