Factoring Trinomials of the Type ax2 + bx + c

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Factoring Trinomials of the Type ax2 + bx + c ALGEBRA 1 LESSON 9-6 (For help, go to Lessons 9-2 and 9-5.) Find the greatest common factor. 1. 12x2 + 6x 2. 28m2 – 35m + 14 3. 4v3 + 36v2 + 10 Factor each expression. 4. x2 + 5x + 4 5. y2 – 3y – 28 6. t2 – 11t + 30 Check Skills You’ll Need 9-6

Factoring Trinomials of the Type ax2 + bx + c ALGEBRA 1 LESSON 9-6 Solutions 1. 12x2 + 6x 12x2 = 2 • 2 • 3 • x • x; 6x = 2 • 3 • x; GCF = 2 • 3 • x = 6x 2. 28m2 – 35m + 14 28m2 = 2 • 2 • 7 • m • m; 35m = 5 • 7 • m; 14 = 2 • 7; GCF = 7 3. 4v3 + 36v2 + 10 4v3 = 2 • 2 • v • v • v; 36v2 = 2 • 2 • 3 • 3 • v • v; 10 = 2 • 5; GCF = 2 4. Factors of 4 with a sum of 5: 1 and 4 x2 + 5x + 4 = (x + 1)(x + 4) 5. Factors of –28 with a sum of –3: 4 and –7 y2 – 3y – 28 = (y – 7)(y + 4) 6. Factors of 30 with a sum of –11: –5 and –6 t2 – 11t + 30 = (t – 5)(t – 6) 9-6

Factoring Trinomials of the Type ax2 + bx + c ALGEBRA 1 LESSON 9-6 Factor 20x2 + 17x + 3. 20x2 + 17x + 3 F O I L 1 • 20 1 • 3 + 1 • 20 = 23 1 • 3 1 • 1 + 3 • 20 = 61 3 • 1 factors of a factors of c 2 • 10 2 • 3 + 1 • 10 = 16 1 • 3 2 • 1 + 3 • 10 = 32 3 • 1 4 • 5 4 • 3 + 1 • 5 = 17 1 • 3 20x2 + 17x + 3 = (4x + 1)(5x + 3) Quick Check 9-6

Factoring Trinomials of the Type ax2 + bx + c ALGEBRA 1 LESSON 9-6 Factor 3n2 – 7n – 6. 3n2 –7n –6 (1)(3) (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) 3n2 – 7n – 6 = (n – 3)(3n + 2) Quick Check 9-6

Factoring Trinomials of the Type ax2 + bx + c ALGEBRA 1 LESSON 9-6 Quick Check Factor 18x2 + 33x – 30 completely. 18x2 + 33x – 30 = 3(6x2 + 11x – 10) Factor out the GCF. Factor 6x2 + 11x – 10. 6x2 + 11x –10 (2)(3) (2)(–10) + (1)(3) = –17 (1)(–10) (2)(1) + (–10)(3) = –28 (–10)(1) (2)(–5) + (2)(3) = –4 (2)(–5) (2)(2) + (–5)(3) = –11 (–5)(2) (2)(–2) + (5)(3) = 11 (5)(–2) 6x2 + 11x – 10 = (2x + 5)(3x – 2) 18x2 + 33x – 30 = 3(2x + 5)(3x – 2) Include the GCF in your final answer. 9-6

Factoring Trinomials of the Type ax2 + bx + c ALGEBRA 1 LESSON 9-6 Factor each expression. 1. 3x2 – 14x + 11 2. 6t2 + 13t – 63 3. 9y2 – 48y – 36 (x – 1)(3x – 11) (2t + 9)(3t – 7) 3(3y + 2)(y – 6) 9-6

Factoring Special Cases ALGEBRA 1 LESSON 9-7 (For help, go to Lessons 8–4 and 9-4.) Simplify each expression. 1. (3x)2 2. (5y)2 3. (15h2)2 4. (2ab2)2 Simplify each product. 5. (c – 6)(c + 6) 6. (p – 11)(p – 11) 7. (4d + 7)(4d + 7) Check Skills You’ll Need 9-7