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Lesson Plan: Teaching Polynomial Equations Grade Level: High School (Grades 9-12) Subject: Algebra Duration: 90 minutes Lesson Objectives: By the end of the lesson, students will be able to: 1. Define polynomial equations. 2. Identify the degree and leading coefficient of a polynomial. 3. Classify polynomials based on their degree. 4. Solve polynomial equations by factoring, using the quadratic formula, and synthetic division. Materials Needed: • Whiteboard and markers • Projector and computer • Graphing calculators • Handouts with practice problems • Polynomials worksheet • Algebra tiles (optional) Lesson Outline: 1. Introduction (10 minutes) • Greet the students and introduce the topic of polynomials. • Briefly explain what polynomials are: expressions that consist of variables and coefficients, involving operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. • Show simple examples (e.g., 2x2+3x+12x^2 + 3x + 12x2+3x+1) and complex examples (e.g., 4x5−2x3+x−64x^5 - 2x^3 + x - 64x5−2x3+x−6) on the board. 2. Key Concepts (20 minutes) • Terms and Degree: o Define terms of a polynomial (e.g., 2x22x^22x2, 3x3x3x, 1). o Explain the degree of a polynomial (highest power of the variable). o Define the leading coefficient (coefficient of the term with the highest degree). • Classification: o Classify polynomials based on their degree: constant (0), linear (1), quadratic (2), cubic (3), quartic (4), etc. o Give examples for each type and ask students to identify the degree and leading coefficient. 3. Solving Polynomial Equations (30 minutes) • Factoring: o Explain the concept of factoring polynomials. o Show methods such as factoring out the greatest common factor (GCF) and factoring trinomials. o Example: Solve x2−5x+6=0 x^2 - 5x + 6 = 0 x2−5x+6=0 by factoring into (x−2) (x−3) =0 (x-2) (x-3) = 0 (x−2) (x−3) =0, then solving x=2 x = 2x=2 and x=3x = 3x=3. • Quadratic Formula: o Derive and explain the quadratic formula: x=−b±b2−4ac2ax = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}x=2a−b±b2−4ac. o Solve a quadratic equation using the quadratic formula. o Example: Solve 2x2+4x−6=02x^2 + 4x - 6 = 02x2+4x−6=0. • Synthetic Division: o Introduce synthetic division as a method to divide polynomials. o Provide step-by-step instructions on how to perform synthetic division. o Example: Divide 2x3−3x2+4x−52x^3 - 3x^2 + 4x - 52x3−3x2+4x−5 by