Factoring to Solve Quadratic Equations

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Presentation transcript:

Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10-5 Solve (2x + 3)(x – 4) = 0 by using the Zero Product Property. (2x + 3)(x – 4) = 0 2x + 3 = 0 or x – 4 = 0 Use the Zero-Product Property. 2x = –3 Solve for x. x = – 3 2 or x = 4 Check: Substitute – for x. 3 2 Substitute 4 for x. (2x + 3)(x – 4) = 0 [2(– ) + 3](– – 4) 0 [2(4) + 3](4 – 4) 0 (0)(– 5 ) = 0 1 (11)(0) = 0 10-5

Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10-5 Solve x2 + x – 42 = 0 by factoring. x2 + x – 42 = 0 (x + 7)(x – 6) = 0 Factor using x2 + 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 3x2 – 2x = 21 by factoring. 3x2 – 2x = 21 Subtract 21 from each side. 3x2 – 2x – 21 = 0 (3x + 7)(x – 3) = 0 Factor 3x2 – 2x – 21. 3x + 7 = 0 or x – 3 = 0 Use the Zero-Product Property 3x = –7 Solve for x. x = – or x = 3 7 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.  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 + 1 = x + 2 The length of the material = x + 3 + 1 + 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 x2 + 7x + 10 = 130 Find the product (x + 2) (x + 5). x2 + 7x – 120 = 0 Subtract 130 from each side. (x – 8) (x + 15) = 0 Factor x2 + 7x – 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.  1 in. 10-5

Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10-5 1. Solve (2x – 3)(x + 2) = 0. Solve by factoring. 2. 6 = a2 – 5a 3. 12x + 4 = –9x2 4. 4y2 = 25 –2, 3 2 – 2 3 ± 5 2 –1, 6 10-5