Factoring to Solve Quadratic Solve and check each

Factoring to Solve Quadratic Solve and check each. Equations equation. ALGEBRA 1 LESSON 10 -5 (For help, go to Lessons 2 -2 and 9 -6. ) 1. 6 + 4 n = 2 2. a – 9 = 4 3. 7 q + 16 = – 3 5. 3 p 2 + 32 p + 20 6. 4 x 2 – 21 x – 18 8 Factor each expression. 4. 2 c 2 + 29 c + 14 5 -13

Factoring to Solve Quadratic Equations Solutions ALGEBRA 1 LESSON 10 -5 1. 6 + 4 n = 2 4 n = – 4 n = – 1 Check: 6 + 4(– 1) = 6 + (– 4) = 2 a 2. 8 – 9 = 4 a 8 = 13 a = 104 Check: 104 – 9 = 13 – 9 = 4 8 3. 7 q + 16 = – 3 7 q = – 19 q = – 2 5 7 Check: 7 (– 2 5 ) + 16 = 7(– 7 19 ) + 16 = – 19 + 16 = – 3 7 5 -13

Factoring to Solve Quadratic Equations Solutions (continued) ALGEBRA 1 LESSON 10 -5 4. 2 c 2 + 29 c + 14 = (2 c + 1)(c + 14) Check: (2 c + 1)(c + 14) = 2 c 2 + 28 c + 14 = 2 c 2 + 29 c + 14 5. 3 p 2 + 32 p + 20 = (3 p + 2)(p + 10) Check: (3 p + 2)(p + 10) = 3 p 2 + 30 p + 20 = 3 p 2 + 32 p + 20 6. 4 x 2 – 21 x – 18 = (4 x + 3)(x – 6) Check: (4 x + 3)(x – 6) = 4 x 2 – 24 x + 3 x – 18 = 4 x 2 – 21 x – 18 5 -13

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 5 -13

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. 5 -13

Factoring to Solve Quadratic Equations 1. Solve (2 x – 3)(x + 2) = 0. ALGEBRA 1 LESSON 10 -5 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 ± – 5 -13 5 2