Factoring to Solve Quadratic Solve and check each

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Factoring to Solve Quadratic Solve and check each. Equations equation. ALGEBRA 1 LESSON 10

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 -12

Factoring to Solve Quadratic Equations Solutions ALGEBRA 1 LESSON 10 -5 1. 6 +

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 -12

Factoring to Solve Quadratic Equations Solutions (continued) ALGEBRA 1 LESSON 10 -5 4. 2

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 -12

Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10 -5 Solve (2 x +

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 5 -12

Factoring to Solve Quadratic Equations Solve x + x – 42 = 0 by

Factoring to Solve Quadratic Equations Solve x + x – 42 = 0 by factoring. ALGEBRA 1 LESSON 10 -5 2 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. 5 -12

Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10 -5 Solve 3 x 2

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 + 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 5 -12

Factoring to Solve Quadratic Equations 1. Solve (2 x – 3)(x + 2) =

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 -12 5 2