5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate 42 - |x - 7| if x = -3 2.Find 4.1  (-0.5) Simplify each expression 3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9) 5.A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green? 6. Which of the following is a true statement Standardized Test Practice: ACBD 8/4 < 4/8-4/8 < -8/4-4/8 > -8/4-4/8 > 4/8

Lesson 9-4 Factoring Trinomials: ax 2 + bx + c

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Objectives Factor trinomials of the form ax 2 + bx + c Solve equations of the form ax 2 + bx + c = 0

Vocabulary Prime polynomial– a polynomial that cannot be written as a product of two polynomials with integral coefficients

Working Backwards Start with the answer “Undo” the operation that got you to the answer Keep “undoing” until you get back to the beginning

Factoring ax 2 + bx + c Set up table looking for factors m and n such that mn = ac and m + n = b Group terms with common factors Factor the GCF from each grouping Rewrite as a product Factors of acSum of the factors 1, ac ac + 1

Example 1a Factor In this trinomial,and You need to find two numbers whose sum is 27 and whose product is or 50. Make an organized list of factors of 50 and look for the pair of factors whose sum is 27. Factors of 50 Sum of Factors 1, 50 2, The correct factors are 2 and 25. Write the pattern and

Example 1a cont Group terms with common factors Factor the GCF from each grouping and CheckYou can check this result by multiplying the two factors. Simplify. Answer: Distributive Property FOIL method FOIL

Example 1b The correct factors are –4, –18. Factor In this trinomial,and Since b is negative, is negative. Since c is positive, mn is positive. So m and n must both be negative. Therefore, make a list of the negative factors of or 72, and look for the pair of factors whose sum is –22. –73 –38 –27 –22 –1, –72 –2, –36 –4, –24 –4, –18 Sum of Factors Factors of 72 Write the pattern and

Example 1b cont and Group terms with common factors Factor the GCF from each grouping Distributive Property Answer:

Example , 8 2, 4 Sum of Factors Factors of 8 Factor Notice that the GCF of the terms, and 32 is 4. When the GCF of the terms of a trinomial is an integer other than 1, you should first factor out this GCF. Distributive Property Now factorSince the lead coefficient is 1, find the two factors of 8 whose sum is 6. The correct factors are 2 and 4 Answer: So,Thus, the complete factorization ofis

Example 3 14 –14 2 –2 –1, 15 1, –15 –3, 5 3, –5 Sum of Factors Factors of –15 Factor In this trinomial,and Since b is positive, is positive. Since c is negative, mn is negative, so either m or n is negative, but not both. Therefore, make a list of all the factors of 3(–5) or –15, where one factor in each pair is negative. Look for the pair of factors whose sum is 7. There are no factors whose sum is 7. Therefore, cannot be factored using integers. Answer:is a prime polynomial.

Example 4 Solve Original equation Rewrite so one side equals 0. Factor the left side. orZero Product Property Solve each equation. Answer: The solution set is

Example 5 Model Rockets Ms. Nguyen’s science class built an air-launched model rocket for a competition. When they test-launched their rocket outside the classroom, the rocket 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 Vertical motion model

Example 5 cont Subtract 30 from each side. Factor out –4. Divide each side by –4. Factor orZero Product Property Solve each equation. The solutions are 0.5 and 3.5 seconds. The first time represents how long it takes the rocket to reach a height of 30 feet on its way up. The second time represents how long it will take for the rocket to reach the height of 30 feet again on its way down. Thus the rocket will be in flight for 3.5 seconds before coming down again. Answer: 3.5 seconds

Summary & Homework Summary: –Factoring as ax 2 + bx + c: Find m and n whose product is ac and whose sum is b. Then write as ax 2 + mx + nx + c and use factoring by grouping Homework: –Pg , 36-40, even