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5-Minute Check on Chapter 2

Transparency 3-1. 5-Minute Check on Chapter 2. Evaluate 42 - |x - 7| if x = -3 Find 4.1  (-0.5) Simplify each expression 3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9)

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5-Minute Check on Chapter 2

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  1. Transparency 3-1 5-Minute Check on Chapter 2 • Evaluate 42 - |x - 7| if x = -3 • Find 4.1  (-0.5) • Simplify each expression • 3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9) • 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 notgreen? • Which of the following is a true statement Standardized Test Practice: 8/4 < 4/8 -4/8 < -8/4 -4/8 > -8/4 -4/8 > 4/8 A B C D Click the mouse button or press the Space Bar to display the answers.

  2. Lesson 9-2 Factoring Using the Distributive Property

  3. Transparency 2 Click the mouse button or press the Space Bar to display the answers.

  4. Transparency 2a

  5. Objectives • Factor polynomials by using the Distributive property • Solve quadratic equations of the form ax2 + bx = 0

  6. Vocabulary • Factoring- to express the polynomial as the product of monomials and polynomials • Factoring by grouping– the use of the Distributive Property to factor some polynomials having four or more terms

  7. Addition and Subtraction PoE Properties of Equality (PoE) are based on the concept that as long as you do the same thing to both sides of an equation, then you have not changed anything. • Addition PoE • For any numbers a, b, and c, if a = b, then a + c = b + c • You can add the same thing to both sides of an equation without changing it. • Subtraction PoE • For any numbers a, b, and c, if a = b, then a - c = b - c • You can subtract the same thing from both sides of an equation without changing it.

  8. Factoring by Grouping • A polynomial can be factored by grouping if all of the following situations exist: • There are four or more terms • Terms with common factors can be grouped together • The two common factors are identical or additive inverses of each other • In Symbols:ax + bx + ay + by = x(a + b) + y(a + b) = (x + y)(a + b)

  9. Zero Product Property • If the product of two factors is 0, then at least one of the factors must be 0 • In Symbols:If ab = 0 then either a = 0, b = 0 or both

  10. Answer: The completely factored form of is Use the Distributive Property to factor . First, find the CGF of 15x and . Factor each number. GFC: Rewrite each term using the GCF. Simplify remaining factors. Distributive Property Example 1a Circle the common prime factors. Write each term as the product of the GCF and its remaining factors. Then use the Distributive Property to factor out the GCF.

  11. Use the Distributive Property to factor . Factor each number. GFC: or Rewrite each term using the GCF. Distributive Property Answer: The factored form of is Example 1b Circle the common prime factors.

  12. Factor Group terms with common factors. Factor the GCFfrom each grouping. Answer: Distributive Property Example 2

  13. Factor Group terms with common factors. Factor GCF from each grouping. Answer: Distributive Property Example 3

  14. Solve Then check the solutions. If , then according to the Zero Product Property either or Original equation or Set each factor equal to zero. Solve each equation. Answer: The solution set is Example 4

  15. Solve Then check the solutions. Write the equation so that it is of the form Original equation Subtract from each side. Factor the GCF of 4y andwhich is 4y. Zero Product Property or Solve each equation. Answer: The solution set is Check by substituting 0 and for y in the original equation. Example 5

  16. Summary & Homework • Summary: • Find the greatest common factor and then use the Distributive Property • With four or more terms, trying factoring by grouping. Factoring by Grouping: ax + bx + ay + by = x(a +b) + y(a +b)= (a +b)(x +y) • Factoring can be used to solve some problems. • Homework: • Pg. 484 16-36 even 48,52,58

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