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# Algebra 9.4

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### Algebra 9.4

1. 1. Warm-Up Exercises Lesson 9.4 Part 11. Find the GCF of 12 and 28.ANSWER 42. Find the GCF of 18 and 42.ANSWER 6
2. 2. Warm-Up Exercises Lesson 9.43. The number (in hundreds) of sunscreen and sun tanning products sold at a pharmacy from 2005-2011 can be modeled by –0.8t2 + 0.3t + 107, where t is the number of years since 2005. About how many products were sold in 2008?ANSWER about 10,070
3. 3. EXAMPLE 1Exercises zero-product property Warm-Up Use theNeed to know!*The solutions of a Polynomial Equation are called roots.*A Polynomial Equation is an equation where one side of the equalsign is a product of polynomial factors and the other side is 0.Example: (x + 2)(x - 6) = 0The Zero-Product Property is used to solve polynomial equations.It states that one of the polynomials must be equal to zero if thewhole equation is equal to zero.
4. 4. EXAMPLE 1Exercises zero-product property Warm-Up Use the Solve (x – 4)(x + 2) = 0. (x – 4)(x + 2) = 0 Write original equation. x – 4 = 0 or x + 2 = 0 Zero-product property x = 4 or x=–2 Solve for x. ANSWER The solutions of the equation are 4 and –2.
5. 5. Warm-Up ExercisesGUIDED PRACTICE for Example 11. Solve the equation (x – 5)(x – 1) = 0. (x – 5)(x – 1) = 0 Write original equation. x – 5 = 0 or x – 1 = 0 Zero-product property x = 5 or x=1 Solve for x. ANSWERThe solutions of the equation are 5 and 1.
6. 6. EXAMPLE 2Exercises greatest common monomial factor Warm-Up Find theYou may need to factor the polynomial before you can use theZero-Product Property to solve the equation. To factor it, lookfor a GCF (a monomial with an integer coefficient) that divides EVENLYinto each term. Factor out the greatest common monomial factor. a. 12x + 42y SOLUTION a. The GCF of 12 and 42 is 6. The variables x and y have no common factor. So, the greatest common monomial factor of the terms is 6. ANSWER 12x + 42y = 6(2x + 7y)
7. 7. EXAMPLE 2Exercises greatest common monomial factor Warm-Up Find the Factor out the greatest common monomial factor. b. 4x4 + 24x3 SOLUTION b. The GCF of 4 and 24 is 4. The GCF of x4 and x3 is x3. So, the greatest common monomial factor of the terms is 4x3. ANSWER 4x4 + 24x3 = 4x3(x + 6)
8. 8. Warm-Up ExercisesGUIDED PRACTICE for Example 22. Factor out the greatest common monomial factor from 14m + 35n.SOLUTIONThe GCF of 14 and 35 is 7. The variables m and n haveno common factor. So, the greatest commonmonomial factor of the terms is 7. ANSWER 14m + 35n = 7(2m + 5n)
9. 9. EXAMPLE 3Exercises equation by factoring Warm-Up Solve an Solve 2x2 + 8x = 0 by factoring out the GCF first. 2x2 + 8x = 0. Write original equation. 2x(x + 4) = 0 Factor left side. 2x = 0 or x + 4 = 0 Zero-product property x=0 or x=–4 Solve for x. ANSWER The solutions of the equation are 0 and – 4.
10. 10. EXAMPLE 4Exercises equation by factoring Warm-Up Solve an Solve 6n2 = 15n. First there needs to be a zero on one side. 6n2 – 15n = 0 Subtract 15n from each side. 3n(2n – 5) = 0 Factor left side. 3n = 0 or 2n – 5 = 0 Zero-product property 5 n=0 or n= Solve for n. 2 ANSWER 5 The solutions of the equation are 0 and . 2
11. 11. Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4Solve the equation by factoring out the GCF first.3. a2 + 5a = 0. a2 + 5a = 0 Write original equation. a(a + 5) = 0 Factor left side. a=0 or a + 5 = 0 Zero-product property a=0 or a=–5 Solve for x.ANSWERThe solutions of the equation are 0 and – 5.
12. 12. Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4 4. 3s2 – 9s = 0. 3s2 – 9s = 0 Write original equation. 3s(s – 3) = 0 Factor left side. 3s = 0 or s – 3 = 0 Zero-product property s= 0 or s=3 Solve for x. ANSWER The solutions of the equation are 0 and 3.
13. 13. Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 45. Solve 4x2 = 2x. Make sure there is a zero on one side first. 4x2 = 2x Write original equation. 4x2 – 2x = 0 Subtract 2x from each side. 2x(2x – 1) = 0 Factor left side. 2x = 0 or 2x – 1 = 0 Zero-product property 1 x=0 or x= Solve for x. 2ANSWER 1The solutions of the equation are 0 and . 2
14. 14. EXAMPLE 5Exercises multi-step problem Warm-Up Solve a ARMADILLO A startled armadillo jumps straight into the air with an initial vertical velocity of 14 feet per second. After how many seconds does it land on the ground? Vertical Motion Formula 2 h = -16t + vt + s where t is the time (sec.) the object has been in the air, v is the initial vertical velocity (ft./sec.), and s is the initial height (feet).
15. 15. EXAMPLE 5Exercises multi-step problem Warm-Up Solve a SOLUTION STEP 1 Write a model for the armadillo’s height above the ground. h = – 16t2 + vt + s Vertical motion model h = – 16t2 + 14t + 0 Substitute 14 for v and 0 for s. h = – 16t2 + 14t Simplify.
16. 16. EXAMPLE 5Exercises multi-step problem Warm-Up Solve a STEP 2 Substitute 0 for h. When the armadillo lands, its height above the ground is 0 feet. Solve for t. 0 = – 16t2 + 14t Substitute 0 for h. 0 = 2t(–8t + 7) Factor right side. 2t = 0 or –8t + 7 = 0 Zero-product property t=0 or t = 0.875 Solve for t. ANSWER The armadillo lands on the ground 0.875 second after the armadillo jumps.
17. 17. Warm-Up ExercisesGUIDED PRACTICE for Example 56. WHAT IF? In Example 5, suppose the initialvertical velocity is 12 feet per second.After how many seconds does armadillo land on theground? SOLUTION STEP 1 Write a model for the armadillo’s height above the ground. h = – 16t2 + vt + s Vertical motion model h = – 16t2 + 12t + 0 Substitute 12 for v and 0 for s. h = – 16t2 + 12t Simplify.
18. 18. Warm-Up ExercisesGUIDED PRACTICE for Example 5STEP 2Substitute 0 for h. When the armadillo lands, its heightabove the ground is 0 feet. Solve for t. 0 = – 16t2 + 12t Substitute 0 for h. 0 = – 4t(4t – 3) Factor right side.– 4t = 0 or 4t – 3 = 0 Zero-product property t=0 or t = 0.75 Solve for t.ANSWERThe armadillo lands on the ground 0.75 second afterthe armadillo jumps.
19. 19. Lesson Review Warm-Up Exercises Part 1Solve the equation by finding the roots.1. (y + 5 ) (y – 9 ) = 0ANSWER –5,92. (2n + 3 ) (n – 4 ) = 0 ANSWER 3 ,4 – 23. 6x2 =20xANSWER 0, 10 3
20. 20. Lesson Review Warm-Up Exercises For use after Lesson 9.44. 12x2 =18xANSWER 0, 3 25. A dog jumps in the air with an initial velocity of 18 feet per second to catch a flying disc. How long does the dog remain in the air? Use h = – 16t2 + vt + s ANSWER 1.125 sec
21. 21. HomeworkWarm-Up Exercises Homework Due Thursday 3/8 Pages 578 - 579 54, 45 - 3 (x3) REVIEW TOMORROW & QUIZ FRIDAY Sections 1 - 4