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8.7 Factoring ax2 + bx + c Essential Question: What is the process for factoring and solving ax2 + bx + c = 0? ***WHEN LEAD COEFFICIENT IS NOT = 1 5-Minute Check 1 Factor m2 – 13m + 36. A. (m – 4)(m – 9) B. (m + 4)(m + 9) C. (m + 6)(m – 6) D. (m + 6)2 5-Minute Check 2 Solve y2 – 8y – 20 = 0. A. {–4, 3} B. {3, 6} C. {–2, 10} D. {1, 8} Content Standards A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines. A.REI.4b Solve quadratic equations by inspection (e.g., for x2 = 49), 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 a ± bi for real numbers a and b. Mathematical Practices 4 Model with mathematics. Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. • prime polynomial Factor ax2 + bx + c Steps: 1. 2. 3. 4. 5. If possible, simply each term (Factor out GCF) Multiply (a*c) for Step 3 Find 2 Integers that multiply to get (a*c) and add to get b. 1. Set up the T Chart to Find the 2 Integers Set up factored form ( )( ) 1. Don’t forget to add your LEAD COEFFICIENT Simply each binomial, if possible CN1. Factor 5x2 + 27x + 10. Practice 1 Factor 3x2 + 26x + 35. A. (3x + 7)(x + 5) B. (3x + 1)(x + 35) C. (3x + 5)(x + 7) D. (x + 1)(3x + 7) 2 Factor ax + bx + c CN2. Factor 4x2 + 24x + 32. Practice 2 Factor 2x2 + 14x + 20. A. (2x + 4)(x + 5) B. (x + 2)(2x + 10) C. 2(x2 + 7x + 10) D. 2(x + 2)(x + 5) Determine Whether a Polynomial is Prime? CN3. Factor 3x2 + 7x – 5, if possible. Practice 3 Factor 3x2 – 5x + 3, if possible. A. (3x + 1)(x – 3) B. (3x – 3)(x – 1) C. (3x – 1)(x – 3) D. prime Real Life Application Solve Equations by Factoring CN4. ROCKETS Mr. Nguyen’s science class built a model rocket for a competition. When they launched their rocket outside the classroom, the rocket cleared the top of a 60-foot high pole and then landed in a nearby tree. If the launch pad was 2 feet above the ground, the initial velocity of the rocket was 64 feet per second, and the rocket landed 30 feet above the ground, how long was the rocket in flight? Use the equation h = –16t2 + vt + h0. End of lesson Homework: • Write Cornell Notes Summary • Unit 5 Homework Packet WHAT TO DO DAILY… • Review Cornell Notes • BRING CALCULATORS • CHECK YOUR MATH CALENDARS