Lesson Plan : Solving Polynomial Equations

Teacher Name:
 Emily Werner
Grade:
 Grade 11-12
Subject:
 Math

Topic:
 Solving Polynomial Equations
Content:
 graphing, sum and difference of cubes, complex roots, quadratic forms, factoring
Goals:
 Teach students how to solve polynomial equations by graphing, using sum and difference of cubes, using the quadratic formula,using a quadratic form, and factoring.
Objectives:
 1) Students will start solving polynomial equations by graphing. 2) Students will begin rewriting sum and difference of cubes, and using sum and difference of cubes to solve polynomials 3) Students will get more practice with the quadratic formula and finding complex roots 4) Students will begin recognizing whn they can rewrite a polynomial in a quadratic form. 5) Students will begin rewriting a polynomial in a factored form,and then get more practice factoring.
Materials:
 overhead, transparencies, overhead markers, whiteboard, whiteboard markers, overhead calculator
Introduction:
 Teacher has students discuss the different ways that they used to solve quadratics. Teacher informs students that many of those ways work to solve polynomials.
Development:
 Teacher starts by teaching students how to solve polynomials by graphing using the overhead calculator. Next the teacher teaches the students how to rewrite the sum and difference of cubes expressions. The teacher teaches the students how to find complex roots of polynomials by first using sum and difference of cubes. Teacher teaches students how to rewrite polynomials in a quadratic form,then factor using that quadratic form. Finally, teacher teaches students how to solve polynomials using a quadratic form.
Practice:
 A; Ex.1: a)Graph (x^2)+2x+4=x+6 b) " (X^3)-19x=-2(x^2)+20 Ex.2: Sum and Difference of Cubes a)(x^3)+8 b)(x^3)-27 c)(x^3)+64 d)(x^3)-125 Ex.3: Find complex roots a) 8(x^3)+125=0 b) 27(x^3)-64=0 B; Ex.1: Factor using a quadratic form a) (x^4)-6(x^2)-27 b) (x^4)+4(x^2)-32 Ex.2: Solve using a quadratic form a) (x^4)-4(x^2)-45=0 b) (x^4)+2(x^2)-24=0
Accommodations:
 verbal and visual directions and explanations, different colors, technology
Checking For Understanding:
 Teacher asks for student input throughout the lecture, teacher asks students questions to get at their understanding, teacher assigns homework.
Closure:
 Teacher gives homework assignment, teacher reminds students to show all work, and teacher reminds students that they can use their notes while they're working.

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