Factoring to Solve Quadratic Equations

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Presentation transcript:

Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10-5 (For help, go to Lessons 2-2 and 9-6.) Solve and check each equation. 1. 6 + 4n = 2 2. – 9 = 4 3. 7q + 16 = –3 Factor each expression. 4. 2c2 + 29c + 14 5. 3p2 + 32p + 20 6. 4x2 – 21x – 18 a 8 5-12

Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10-5 Solutions 1. 6 + 4n = 2 4n = –4 n = –1 Check: 6 + 4(–1) = 6 + (–4) = 2 2. – 9 = 4 = 13 a = 104 Check: – 9 = 13 – 9 = 4 3. 7q + 16 = –3 7q = –19 q = –2 Check: 7 (–2 ) + 16 = 7(– ) + 16 = –19 + 16 = –3 a 8 a 8 104 8 5 7 5 7 19 7 5-12

Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10-5 Solutions (continued) 4. 2c2 + 29c + 14 = (2c + 1)(c + 14) Check: (2c + 1)(c + 14) = 2c2 + 28c + c + 14 = 2c2 + 29c + 14 5. 3p2 + 32p + 20 = (3p + 2)(p + 10) Check: (3p + 2)(p + 10) = 3p2 + 30p + 2p + 20 = 3p2 + 32p + 20 6. 4x2 – 21x – 18 = (4x + 3)(x – 6) Check: (4x + 3)(x – 6) = 4x2 – 24x + 3x – 18 = 4x2 – 21x – 18 5-12

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 5-12

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. 5-12

Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10-5 Solve 3x2 – 2x = 21 by factoring. 3x2 – 2x = 21 Subtract 21 from each side. (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 5-12

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 5-12