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Unit 3: Instructional Strategies and Resources Video demonstration of concept and example problems: Demonstration: Kuta worksheet: - Long Division Sample problems, video demo, and attached quiz: Demonstration video: Steps and sample problems (seen above): Video demonstration: Sample Notes and examples: Notes and examples: : Synthetic Division Common Core State Standard Rewrite rational expressions A-APR.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. Objectives/Skills - Use synthetic division to show factors of polynomials. Sample problems, notes: In-class problems for practice, answers can be revealed: Khan Academy video: Notes and example demonstration: The Factor TheoremCommon Core State Standard Understand the relationship between zeros and factors of polynomials A-APR.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). A-APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Objectives/Skills Show that x – a and x – b is a factor of the polynomial using the Factor Theorem Bottom of this worksheet has Factor Theorem Quick note and sample problems: Demonstration video: Demonstration video: Demonstration video: : Solve Quadratic Equations by Factoring Common Core State Standard A.REI.4 – a. use the method of completing the square to transform any quadratic equation in x into an equation of the form that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for ), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as for real numbers a and b. A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ a. Factor a quadratic expression to reveal the zeros of the function it defines. Objectives/Skills - Factor a quadratic expression to find the zeros of the function it represents. -Write a quadratic equation with given zeros. GCF Flipchart: Special Products Flipchart: Websites: ebra1/module8-6.html .htm Videos: (includes videos in Spanish) i/inter/student/olc/graphics/dugopolski03ia_s/ch0 5/others/ch05-9.pdfNovember 2, 2015 – November 6, 2015Concept: Polynomial Functions (The Remainder) Common Core State Standard Understand the relationship between zeros and factors of polynomials A-APR.239 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).Websites: Notes with examples: ainder_theorem Problems – answers can be revealed one step at a time: _6_8.htmlConcept: Graphing Quadratic Functions Common Core State Standard Analyze functions using different representations F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ Graph linear and quadratic functions and show intercepts, maxima, and minima. Objectives/Skills Define and graph a quadratic function identify the parts of a quadratic function. Identify and write the equation of the axis of symmetry. Identify the y-intercept. o Identify the vertex. o Find the maximum and minimum values. -- tutorial and notes -- tutorial with examples -- notes page with practice problems and multiple choice questions ................
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