Curated OER
Polynomials and Linear Factors
This algebra worksheet reviews writing polynomials in standard form from factored form, looks at the graphs of polynomials of degree higher than two, and identifies the zeros of polynomials using the Factor Theorem and Fundamental...
Curated OER
The Remainder and Factor Theorems
In this remainder and factor theorems worksheet, 11th graders solve and complete 10 different problems. First, they divide using synthetic division and write their answer in the form given. Then, students use synthetic division to find...
Curated OER
Using Synthetic Substitution and The Factor Theorem to determine Factors of Polynomials
In this synthetic substitution worksheet, students evaluate three different function at specified points. Students also determine if given factors are factors of four specific polynomials. Additionally students use the Factor...
Curated OER
The Remainder Theorem
In this algebra worksheet provides extra practice on using the Remainder Theorem to find a factor of a higher degree polynomial. It provides a good review of synthetic division. There are 22 problems with an answer key.
Centre for Education in Mathematics and Computing
Roots and the Pythagorean Theorem
In this roots and the Pythagorean Theorem worksheet, learners solve 15 different types of problems related to square roots and applying the Pythagorean Theorem. They first determine the square root of each number and then, the cube root....
EngageNY
Fundamental Theorem of Similarity (FTS)
How do dilated line segments relate? Lead the class in an activity to determine the relationship between line segments and their dilated images. In the fourth section in a unit of 16, pupils discover the dilated line...
Curated OER
Theory of Polynomials
In this polynomial worksheet provides extra practice the Factor and Remainder Theorems. They identify factors of given linear expressions. This two-page worksheet contains 19 problems. The answers are provided on the second page.
Curated OER
Roots of Polynomial Functions
Here is a unit test on finding factors and zeros of higher-degree polynomials that could be used as a review or practice test. The Remainder Theorem, Rational Zero Theorem, and Factor Theorem are put into use. While this four-page...
Illustrative Mathematics
The Missing Coefficient
This activity highlights the use of the remainder theorem to solve for the unknown coefficient of a specified polynomial when given one of its factors. Use this single problem as a warm-up exercise, a quick check-in at the end of a...
Curated OER
Primes and Prime Factors
In this primes and prime factors activity, 8th graders solve 21 different problems to include identifying each number as prime, composite, or neither prime nor composite and listing all the primes less than 200. Then they complete each...
Illustrative Mathematics
Zeroes and factorization of a quadratic polynomial I
This activity uses the division algorithm and the definition of a zero/root of a function to guide your class to see the relationship between zeros and factors of a general quadratic, which can later be generalized to the Remainder...
Curated OER
Fundamental Theorem of Algebra
In this worksheet, learners identify the Fundamental Theorem of Algebra. They solve polynomial functions and simplify expressions and equations.
Inside Mathematics
Hopewell Geometry
The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...
Curated OER
Dividing Polynomials
In this Algebra II/college level worksheet, students use long and synthetic division to divide polynomials and use the Factor Theorem to show that a given polynomial is a factor of a polynomial function. The two page worksheet...
Flipped Math
Remainder Theorem
Don't divide! Pupils view three examples relating the remainder of a polynomial division and the polynomial function evaluated at a related value. Learners notice how to find a missing coefficient in a polynomial given the remainder of a...
Curated OER
Going Back to Your Roots
Investigate the Fundamental Theorem of Algebra and explore polynomial equations to determine the number of factors, the number of roots, and investigate multiplicity of roots.
Mt. San Antonio Collage
Synthetic Division and Zeros of Polynomial Functions
More than just a worksheet, this guide provides the description of many of the polynomials theorems to assist the learners. Starting with synthetic division, class members are then guided through the remainder theorem and linear...
Curated OER
Calculating Arc Lengths of Simple Functions-I
In this calculating arc lengths worksheet, learners are given 4 simple functions and they use the Pythagorean Theorem and the basic techniques of calculus to find the arc-length formula in order to find the arc-length.
EngageNY
First Consequences of FTS
Challenge the young mathematicians to find the exact coordinates of a dilated point. The fifth segment in a 16-part series introduces the class to the converse of the Fundamental Theorem of Similarity. Scholars use the theorem to...
West Contra Costa Unified School District
Polynomial Division
Multiply the ways your scholars can find the quotient with polynomial division. A lesson introduces polynomial division via long division, synthetic division, generic area model, and using the definition of division. Learners then...
Mt. San Antonio Collage
Quiz 2: Polynomials
Four questions that get right to the polynomial point. High schoolers list all the attributes of a polynomial function, including finding all complex zeros. The last two questions prompt them to write a function based on the given...
West Contra Costa Unified School District
Polynomial Division
How do you apply the traditional division algorithm to polynomials? Here is an Algebra II activity that extends the use of the division algorithm to polynomials. After establishing the concept of long division, synthetic division and the...
EngageNY
Informal Proof of AA Criterion for Similarity
What does it take to show two triangles are similar? The 11th segment in a series of 16 introduces the AA Criterion for Similarity. A discussion provides an informal proof of the theorem. Exercises and problems require scholars to apply...
Curated OER
Number Sense and Numeration: Square Roots
In this square roots activity, 8th graders solve 14 different types of problems to include determining the square root of a number of problems, determining the area of a rectangle and the length of a side of a square with the same...