Download Integrated 2 -‐ Sec 2.03

 Name: __________________________________ Date: _____________________ Integrated 2 -­‐ Sec 2.03 -­‐ Zero Product Property Purpose & Outcome: o To factor expressions using various techniques (by identifying a common factor, using algebra tiles, using distributive property, or regrouping). o To apply the Zero-­‐Product Property to factored expressions. 1. Sasha is thinking of two numbers whose product is 10. Can you guess the numbers she is thinking of? 2. Tony is thinking of two numbers whose product is 0. Can you guess the numbers he is thinking of? 3. Mindy was asked to find all the solutions to the equation (x + 2)(x + 4) = 15. She says, "I can break up the equation into two simpler ones (x + 2)(x + 4) = 15 ⇒ (x + 2) = 15 or (x + 4) = 15 So, there are two answers x = 13 or x = 11." Do you agree with her answers and her reasoning process? Why or why not? 4. Mikey was also asked to solve the same equation (x + 2)(x + 4) = 15. He says, "Since 3 times 5 equals 15. I can break up the equation into two simpler ones (x + 2)(x + 4) = 15 ⇒ (x + 2) = 3 or (x + 4) = 5 So, there is an answer x = 1." Discuss Mikey's method. 5. Wendy was asked to find all the solutions to the equation (x + 1)(x + 2) = 0. She says, "I can break up the equation into two simpler ones (x + 1)(x + 2) = 0 ⇒ (x + 1) = 0 or (x + 2) = 0 So, there are two answers x = -­‐1 or x = -­‐2." Do you agree with her answers and her reasoning process? Why or why not? Zero Product Property (ZPP) 6. Find all the real values of x that make each of the following equations true. a) (x – 4)(x + 5) = 0 b) x(x + 1) = 0 c) (2x + 3)(5 – 4x) = 0 !1
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d) (6x)(x + π) # x + 8& = 0 "2
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e) x(x – 3)(x2 + 3) = 0 f) x2 + 2x = 0 7. What does it mean to factor a number such as 6? Do you have an image that would be helpful to visualize the factors of a number? 8. Using algebra tiles, shade in the figure below to show how to factor the expression x2 + 2x. Convention for algebra tiles: x
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9. Factor the expression on the left side of the each equation over the integers and solve the equation using the Zero-­‐Product Property. Use algebra tiles to factor if necessary and applicable. a) 2x2 + 6x = 0 b) 3x2 + 5x = 0 c) 4x3 + x2 = 0 d) x2 + 3x + 2 = 0 e) 2x2 + 7x + 3 = 0 f) x2 – 3x – 4= 0 g) 2(x + 1) + x(x + 1) = 0 h) (x2 + 1)(x – 7) + (3x)( x2 + 1) = 0 i) x3 + x2 – 3x – 3= 0 j) 3x3 – 5x2 – 15x + 25= 0 10. Joseph was asked to solve the equation x3 = 5x. He wonders if he can just divide by x in the beginning. He says, "Well, there is an x on each side, so I can just divide then solve it from there." His solution is shown below. Do you agree with his solution? Why or why not? If you disagree, show how you would solve the problem? x3 = 5x x 3 5x
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x2 = 5 x = 5 11. Larry was asked to factor the expression 10x2 + 14x – 12 over the integers. He knew that one of the factors is x + 2. Find the other factor(s). 12. Solve the given equation for x: 10x2 + 14x = 12 Bonus: Solve the inequalities: a) x(x – 3) ≥ 0 b) (x – 2)(x + 1) < 0