Factoring Trinomials of the Type 2 bx c

Factoring Trinomials of the Type 2 + bx + c ax Find the greatest common factor. ALGEBRA 1 LESSON 9 -6 (For help, go to Lessons 9 -2 and 9 -5. ) 1. 12 x 2 + 6 x 2. 28 m 2 – 35 m + 14 3. 4 v 3 + 36 v 2 + 10 Factor each expression. 4. x 2 + 5 x + 4 5. y 2 – 3 y – 28 5 -9 6. t 2 – 11 t + 30

Factoring Trinomials of the Type ax 2 + bx + c Solutions ALGEBRA 1 LESSON 9 -6 1. 12 x 2 + 6 x 12 x 2 = 2 • 3 • x; 6 x = 2 • 3 • x; GCF = 2 • 3 • x = 6 x 2. 28 m 2 – 35 m + 14 28 m 2 = 2 • 7 • m; 35 m = 5 • 7 • m; 14 = 2 • 7; GCF = 7 3. 4 v 3 + 36 v 2 + 10 4 v 3 = 2 • v • v; 36 v 2 = 2 • 3 • v • v; 10 = 2 • 5; GCF = 2 4. Factors of 4 with a sum of 5: 1 and 4 x 2 + 5 x + 4 = (x + 1)(x + 4) 5. Factors of – 28 with a sum of – 3: 4 and – 7 y 2 – 3 y – 28 = (y + 4)(y – 7) 6. Factors of 30 with a sum of – 11: – 5 and – 6 t 2 – 11 t + 30 = (t – 5)(t – 6) 5 -9

Factoring Trinomials of the Type ax 2 + bx + c ALGEBRA 1 LESSON 9 -6 Factor 20 x 2 + 17 x + 3 F O I L factors 1 • 20 of a 1 • 3 + 1 • 20 = 23 1 • 1 + 3 • 20 = 61 1 • 3 3 • 1 2 • 10 2 • 3 + 1 • 10 = 16 2 • 1 + 3 • 10 = 32 1 • 3 3 • 1 4 • 5 4 • 3 + 1 • 5 = 17 1 • 3 20 x 2 + 17 x + 3 = (4 x + 1)(5 x + 3) 5 -9 factors of c

Factoring Trinomials of the Type ax 2 + bx + c ALGEBRA 1 LESSON 9 -6 Factor 3 n 2 – 7 n – 6. 3 n 2 (1)(3) – 7 n – 6 (1)(– 6) + (1)(3) = – 3 (1)(– 6) (1)(1) + (– 6)(3) = – 17 (– 6)(1) (1)(– 3) + (2)(3) = 3 (2)(– 3) (1)(2) + (– 3)(3) = – 7 (– 3)(2) 3 n 2 – 7 n – 6 = (n – 3)(3 n + 2) 5 -9

Factoring Trinomials of the Type ax 2 + bx + c ALGEBRA 1 LESSON 9 -6 Factor 18 x 2 + 33 x – 30 completely. 18 x 2 + 33 x – 30 = 3(6 x 2 + 11 x – 10) Factor out the GCF. Factor 6 x 2 + 11 x – 10. 6 x 2 (2)(3) + 11 x (2)(– 10) + (1)(3) = – 17 – 10 (1)(– 10) (2)(1) + (– 10)(3) = – 28 (– 10)(1) (2)(– 5) + (2)(3) = – 4 (2)(2) + (– 5)(3) = – 11 (2)(– 5)(2) (2)(– 2) + (5)(3) = 11 (5)(– 2) 6 x 2 + 11 x – 10 = (2 x + 5)(3 x – 2) 18 x 2 + 33 x – 30 = 3(2 x + 5)(3 x – 2) 5 -9 Include the GCF in your final answer.

Factoring Trinomials of the Type 2 + bx + c ax Factor each expression. ALGEBRA 1 LESSON 9 -6 1. 3 x 2 – 14 x + 11 (x – 1)(3 x – 11) 2. 6 t 2 + 13 t – 63 (2 t + 9)(3 t – 7) 3. 9 y 2 – 48 y – 36 3(3 y + 2)(y – 6) 5 -9