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Dividing by (x – a) and (x + a)
Patterns in math emerge from seemingly random places. Learners explore the patterns for factoring the sum and differences of perfect roots. Analyzing these patterns helps young mathematicians develop the polynomial identities.
Curated OER
Greatest Common Factor and Factoring by Grouping
In this Algebra II/college level worksheet, young scholars factor polynomials by pulling out the GCF and by grouping. The two page worksheet contains seventy–two problems. Answers are provided.
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Multiplying Polynomials using the Distributive property.
Students factor polynomial functions. In this algebra lesson plan, students solve problems through factoring and distribution of the negative sign correctly.
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Using CAS and algebra tiles with Expanding and factoring trinomials
Ninth graders investigate multiplication of binomials and factoring of trinomials. In this Algebra I instructional activity, 9th graders compare and contrast expansion and factoring using algebra tiles and a TI-89.
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Multiplying Polynomials - FOIL
Students participate in an activity to demonstrate the distributive property. They take notes as they observe different methods of FOIL. Afterward, students work on their own, and in groups to determine which method to use and complete...
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Special Products of Polynomials
In this polynomial worksheet, students use FOIL to multiply polynomials. Polynomials involve four to five terms, some with fractions. There are 30 problems on this two-page worksheet.
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Multiplication of Polynomials
In this polynomial worksheet, 10th graders multiply polynomial equations. Equations contain between two to six terms. There are 22 problems on this two-page worksheet.
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Quadratic Equations with Negative Discriminate
Solve polynomial equations of degree using different theorems and apply the zero factor theorem for unknown numbers in a quadratic equation. Also use the discriminate to find out the kind of solutions to given quadratic equations shown.
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Elementary Algebra Study Guide
Middle and high schoolers solve problems involving linear equations, inequalities, quadratics, radicals, systems of equations, exponents, and polynomials. Many of the problems encompass a review of Algebra I. This 10-page worksheet...
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How Simple Is Your Rational Expression?
Investigate simplifying rational expressions. Learners define rational expressions, review how numerators and denominators are polynomials and complete several problems using a checklist to ensure they don't skip any steps. Work can be...
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College Level Study Guide
In this study guide worksheet, students examine and complete questions that are similar to the college Accuplacer College Level Math test. This worksheet includes, but is not limited to, factoring and expanding polynomials, simplifying...
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Factoring
Young scholars factor quadratic equations into two binomials multiplied by each other. In this quadratic equations lesson plan, students complete math problems in and out of class.
Willow Tree
Solving Quadratic Equations
Polynomials are full of solutions! Learners understand that the degree determines the number of solutions. Examples show quadratic equations solved by factoring and by using the quadratic formula. A cubic equation is even mixed in for...
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Factoring Trinomials
Learners factor trinomials using specific factoring methods. In this algebra lesson, students factor equations using the difference of squares and foiling. They play a game to enhance their understanding of factoring.
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Factoring Trinomials
Young scholars factor trinomials and other quadratic functions. In this algebra instructional activity, students solve trinomials containing negative and positive coefficients. They factor quadratics of difference squares as well as...
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Multiply Polynomials
Learners solve polynomial problems. In this algebra lesson, students multiply polynomial equations using FOIL and quadratic formula. They complete the square and factor by grouping.
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Graphing Polynomials
Students graph polynomial equations using different methods. In this algebra lesson, students identify the different ways the x and y values relate in a graph. They solve for x by finding the zero's of the polynomials.
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10-4 Practice: Factoring Differences of Squares
In this practice worksheet, students factor the differences of squares and identify prime expressions. Polynomials contain one or more variables, with exponents. Students complete 42 problems. An answer key is provided.
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Worksheet #11: Dividing Polynomials
In this multiple choice polynomial worksheet, students complete 20 problems involving division of polynomials and reduce them to their lowest terms.
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Factoring Trinomials
Students factor trinomials using algebra tiles and blocks. In this algebra lesson plan, students complete a trinomials station activity. They work backwords to find their answers and discuss their steps in a group.
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Quadratic Equations and Functions
This comprehensive lesson plan reviews solving and graphing quadratic functions and functions of higher degree. Using the vertex form of a quadratic functions, one finds the vertex, minimum or maximum, and axis of symmetry. A few word...
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Using Electronic Manipulatives in Multiplication
Factor polynomials using electronic manipulatives. Your class will create a spreadsheet in excel and use it to multiply and perform basic operations and solve problems correctly. They create a visual to go along with each multiplication...
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...
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Overcoming a Third Obstacle to Factoring— What If There Are No Real Number Solutions?
Time for pupils to use their imagination! Learners examine the relationship between a system with no real solution and its graph. They then verify their discoveries with algebra.