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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 9-3 Factoring Trinomials: x2 + bx + c

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

  4. Transparency 3a

  5. Objectives • Factor trinomials of the form x2 + bx + c • Solve equations of the form x2 + bx + c = 0

  6. Vocabulary • none – means nothing.

  7. Factoring x2 + bx + c • To factor quadratic trinomials of the form x2 + bx + c, find two integers, m and n, whose sum is equal to b and whose product is equal to c. • Then write x2 + bx + c using the pattern (x + m)(x + n) • Symbols: x2 + bx + c = (x + m)(x + n)when m + n = b and m  n = c • Examples: • x2 + 5x + 6 = (x + 2)(x + 3), since 2 + 3 = 5 and 2  3 = 6 • x2 + 7x + 10 = (x + 2)(x + 5), since 2 + 5 = 7 and 2  5 = 10 • x2 + 9x + 18 = (x + 3)(x + 6), since 3 + 6 = 9 and 3  6 = 18

  8. Multiplication and Division 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. • Multiplication PoE • For any numbers a, b, and c, if a = b, then ac = bc • You can multiply both sides of an equation by the same thing without changing the equation • Division PoE • For any numbers a, b, and c with c ≠ 0, if a = b, then a/c = b/c • You can divide both sides of an equation by the same thing without changing the equation • Multiplication and division are reciprocal actions

  9. Factor In this trinomial, and You need to find the two numbers whose sum is 7 and whose product is 12. Make an organized list of the factors of 12, and look for the pair of factors whose sum is 7. Write the pattern. and Answer: Example 1 The correct factors are 3 and 4.

  10. F O I L FOIL method Simplify. Example 1 cont Check You can check the result by multiplying the two factors.

  11. Factor In this trinomial, and This means is negative and mn is positive. So m and n must both be negative. Therefore, make a list of the negative factors of 27, and look for the pair whose sum is –12. Write the pattern. Answer: and Example 2 The correct factors are –3 and –9.

  12. Check You can check this result by using a graphing calculator. Graph andon the same screen. Since only one graph appears, the two graphs must coincide. Therefore, the trinomial has been factored correctly. Example 2 cont

  13. Write the pattern. Factor In this trinomial, and This means is positive and mn is negative, so either m or n is negative, but not both. Therefore, make a list of the factors of –18 where one factor of each pair is negative. Look for the pair of factors whose sum is 3. and Answer: Example 3 The correct factors are –3 and 6.

  14. Write the pattern. Factor Since and is negative and mn is negative. So either m or n is negative, but not both. and Answer: Example 4 The correct factors are 4 and –5.

  15. Solve Original equation Rewritethe equation so that one side equals 0. or Factor. Zero Product Property Solve each equation. Answer: The solution is Example 5

  16. Example 6 ArchitectureMarion has a small art studio measuring 10 feet by 12 feet in her backyard. She wants to build a new studio that has three times the area of the old studio by increasing the length and width by the same amount. What will be the dimensions of the new studio? Explore Begin by making a diagram like the one shown to the right, labeling the appropriate dimensions.

  17. Write the equation. Solve Multiply. Plan Let the amount added to each dimension of the studio. old area Subtract 360 from each side. Example 6 cont The new length times the new width equals the new area.

  18. Factor. Zero Product Property or Solve each equation. Examine The solution set is Only 8 is a valid solution, since dimensions cannot be negative. Answer: The length of the new studio should be or 20 feet and the new width should be or 18 feet. Example 6 cont

  19. Summary & Homework • Summary: • Factoring x2 + bx +c: Find m and n whose sum is b and whose product is c. • Then write x2 + bx + c as (x + m)(x + n) • Homework: • Pg. 493. 18-34 even, 38,40,48

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