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Worksheet
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\n\"The\n\n
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\nCurated OER\n
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\nThe Remainder and Factor Theorems\n

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\n\nFor Students\n\n11th\n
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\nIn this remainder and factor theorems activity, 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...\n
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Worksheet
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\n\"Using\n\n
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\nCurated OER\n
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\nUsing Synthetic Substitution and The Factor Theorem to determine Factors of Polynomials\n

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\n\nFor Students\n\n10th - 12th\n
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\nIn this synthetic substitution activity, 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...\n
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Worksheet
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\n\"Polynomials\n\n
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\nCurated OER\n
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\nPolynomials and Linear Factors\n

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\n\nFor Students\n\n10th - 11th\n\nStandards\n
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\nThis 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...\n
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Lesson Plan
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\n\"Watch\n\n
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\nCurated OER\n
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\nWatch Your P's and Q's\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nUsing your graphing calculator, find all the rational zeroes of a polynomials by using the Rational Zero Theorem. Divide polynomials using the Remainder Theorem and the Factor Theorem and then graph it to find the number of real roots.\n
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Lesson Plan
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\n\"Quadratic\n\n
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\nCurated OER\n
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\nQuadratic Equations with Negative Discriminate\n

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\n\nFor Teachers\n\n9th - 11th\n
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\nSolve 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.\n
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Worksheet
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\n\"Dividing\n\n
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\nCurated OER\n
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\nDividing Polynomials\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn this Algebra II/college level instructional activity, 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...\n
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Lesson Plan
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\n\"The\n\n
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\nCurated OER\n
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\nThe Remainder Theorem Using TI-Nspire CAS\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nInvestigate the Remainder Theorem in this algebra lesson. Explore the relationship between the remainders of polynomial division and the function. Each of the four problems gets progressively more complicated. This might be a great...\n
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Worksheet
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\n\"Theory\n\n
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\nCurated OER\n
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\nTheory of Polynomials\n

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\n\nFor Students\n\n9th - 11th\n
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\nIn this polynomial learning exercise provides extra practice the Factor and Remainder Theorems. They identify factors of given linear expressions. This two-page learning exercise contains 19 problems. The answers are provided on the...\n
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Worksheet
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\n\"Roots\n\n
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\nCurated OER\n
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\nRoots of Polynomial Functions\n

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\n\nFor Students\n\n10th - 12th\n
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\nHere 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...\n
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Lesson Plan
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\n\"The\n\n
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\nIllustrative Mathematics\n
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\nThe Missing Coefficient\n

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\n\nFor Teachers\n\n10th - 12th\n\nStandards\n
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\nThis 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...\n
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Activity
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\n\"Zeroes\n\n
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\nIllustrative Mathematics\n
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\nZeroes and factorization of a quadratic polynomial I\n

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\n\nFor Teachers\n\n10th - 12th\n\nStandards\n
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\nThis 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...\n
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Lesson Plan
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\n\"Scale\n\n
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\nEngageNY\n
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\nScale Factors\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nIs it bigger, or is it smaller—or maybe it's the same size? Individuals learn to describe enlargements and reductions and quantify the result. Lesson five in the series connects the creation of a dilated image to the result. Pupils...\n
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Lesson Plan
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\n\"Arithmetic\n\n
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\nCurated OER\n
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\nArithmetic Complex Numbers\n

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\n\nFor Teachers\n\n10th - 11th\n
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\nStudents convert quadratic functions from standard form to vertex form. In this algebra lesson, students solve polynomials using synthetic and long division. They derive and apply the remainder theorem and factor theorem.\n
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Lesson Plan
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\n\"Polynomial\n\n
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\nCurated OER\n
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\nPolynomial Divisions\n

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\n\nFor Teachers\n\n8th - 10th\n
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\nStudents factor polynomials and use long division t solve problems. For this algebra lesson, students find the zeros of polynomials by synthetic and long division. They perform operation using complex numbers.\n
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\n\"Varsity\n\n
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\nVarsity Tutors \n
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\nVarsity Tutors: Hotmath: Polynomial Division: The Remainder and Factor Theorems\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nThirty-nine problems present a variety of practice applying the remainder and factor theorems to polynomial division.\n
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eBook
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\n\"Math\n\n
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\nMath Planet\n
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\nMath Planet: Algebra 2: Polynomial Functions: Remainder and Factor Theorems\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nProvides examples and a video lesson that illustrate the remainder and factor theorems. [1:34]\n
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Activity
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\n\"Purplemath:\n\n
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\nPurple Math\n
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\nPurplemath: Factor Theorem\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nPurplemath.com discusses the Factor Theorem, explaining its relationship to the Remainder Theorem. The lesson has a link to synthetic division, a key to discovering if a value is a root.\n
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Activity
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\n\"Interactive\n\n
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\nInteractive Mathematics\n
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\nInteractive Mathematics: The Remainder and the Factor Theorem\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nThis tutorial contains a lesson about the remainder and factor theorems along with practice problems.\n
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\n\"Glencoe\n\n
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\nMcGraw Hill\n
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\nGlencoe Mathematics: Quiz on the Remainder and Factor Theorems\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nThe online assessment demonstrates knowledge of advanced mathematical concepts in Algebra II. The questions test students on the remainder and factor theorems.\n
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Activity
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\n\"Ojk's\n\n
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\nWindstream\n
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\nOjk's Precalculus Study Page: Remainder and Factor Theorems\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nAn introduction to two important uses of synthetic substitution, the remainder theorem and the factor theorem. Includes examples and sample problems with solutions.\n
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Handout
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\n\"Paul's\n\n
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\nPaul Dawkins\n
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\nPaul's Online Notes: Algebra: Zeroes/roots of Polynomials\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nLearn about the root or zero of a polynomial with this reference guide. Includes definitions, step-by-step instructions on how to find all the zeroes for a given polynomial, and multiple examples. Also included is a description of The...\n
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Unit Plan
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\n\"Real\n\n
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\nRichland Community College\n
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\nReal Zeros of Polynomial Functions\n

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\n\nFor Students\n\n10th - 12th\n\nStandards\n
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\nThis site from the Richland Community College contains information on long and synthetic division, the remainder theorem and the factor theorem.\n
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Activity
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\n\"Wtamu\n\n
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\nTexas A&M University\n
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\nWtamu Virtual Math Lab: College Algebra: Synthetic Division\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nThis tutorial will show you how to use synthetic division and how to use both the remainder and factor theorems in conjunction with synthetic division. Offers several examples with solutions and explanations as well as practice problems...\n
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\n\"Pre\n\n
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\nMath Notes and Math Tests\n
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\nPre Calculus Notes: Polynomial Functions of Higher Degree [Pdf]\n

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\n\nFor Students\n\n9th - 10th\n
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\nThe resource discusses polynomial functions of higher degree. Topics examined are infinity, limits, the factor theorem, and the intermediate value theorem.\n
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\n\nGet Free Access\n\nSee Review\n
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