Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON
Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10 -5 Solve (2 x + 3)(x – 4) = 0 by using the Zero Product Property. (2 x + 3)(x – 4) = 0 2 x + 3 = 0 or x– 4=0 2 x = – 3 3 x=– 2 Use the Zero-Product Property. Solve for x. or x=4 3 Check: Substitute – 2 for x. Substitute 4 for x. (2 x + 3)(x – 4) = 0 [2(– 3 ) + 3](– 3 – 4) 2 2 (2 x + 3)(x – 4) = 0 0 [2(4) + 3](4 – 4) 1 0 (11)(0) = 0 (0)(– 5 2 ) = 0 10 -5
Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10 -5 Solve x 2 + x – 42 = 0 by factoring. x 2 + x – 42 = 0 (x + 7)(x – 6) = 0 Factor using x 2 + x – 42 x+7=0 or x– 6=0 Use the Zero-Product Property. x = – 7 or x=6 Solve for x. 10 -5
Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10 -5 Solve 3 x 2 – 2 x = 21 by factoring. 3 x 2 – 2 x = 21 Subtract 21 from each side. 3 x 2 – 2 x – 21 = 0 (3 x + 7)(x – 3) = 0 3 x + 7 = 0 or Factor 3 x 2 – 2 x – 21. x– 3=0 3 x = – 7 7 x=– 3 Use the Zero-Product Property Solve for x. or x=3 10 -5
Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10 -5 The diagram shows a pattern for an open-top box. The total area of the sheet of materials used to make the box is 130 in. 2. The height of the box is 1 in. Therefore, 1 in. squares are cut from each corner. Find the dimensions of the box. Define: Let x = width of a side of the box. Then the width of the material = x + 1 = x + 2 The length of the material = x + 3 + 1 = x + 5 Relate: length width = area of the sheet 10 -5
Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10 -5 (continued) Write: (x + 2) (x + 5) = 130 x 2 + 7 x + 10 = 130 x 2 + 7 x – 120 = 0 (x – 8) (x + 15) = 0 Find the product (x + 2) (x + 5). Subtract 130 from each side. Factor x 2 + 7 x – 120. x– 8=0 or x + 15 = 0 Use the Zero-Product Property. x=8 or x = – 15 Solve for x. The only reasonable solution is 8. So the dimensions of the box are 8 in. 11 in. 10 -5
Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10 -5 1. Solve (2 x – 3)(x + 2) = 0. 3 – 2, 2 Solve by factoring. 2. 6 = a 2 – 5 a – 1, 6 3. 12 x + 4 = – 9 x 2 4. 4 y 2 = 25 2 3 ± – 10 -5 5 2
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