Section 9-5 Factoring Trinomials SPI 23G: select one of the factors of a quadratic equation Objective: Factor Trinomials Prime factors: numbers that are only divisible by 1 and itself Coefficient: constant in front of a variable Multiply Binomials: (x + 3)(x + 5) = x 2 + 8x + 15 Quadratic equation: the highest exponent is 2; (i.e. x 2 )

Factoring a Quadratic Equation x 2 + bx + c (b and c are constants) into Two Binomials Factor x 2 + 8x (x + 3)(x + 5) How do you get the first term (x 2 )? How do you get the second term (8x)? How do you get the third term (15)? Factors of 15Sum of Factors 1 and and 5 8 x 2 + 8x + 15 = (x + 3)(x + 5). Find the factors of 15.Identify the pair that has a sum of 8. x ∙ x 5x + 3x 3 ∙ 5

Factor g 2 + 7g ∙ ∙ -10 Sum of FactorsFactors of 10 Both conditions must be true Factors of the problem are (g + 2)(g + 5) Factor g 2 - 7g + 10 How does the factors change when you have a negative 2d term? Factors of 10Sum of Factors 1 ∙ ∙ 57 Factors of the problem are (g - 2)(g - 5) Both conditions must be true Factoring a Quadratic Equation

a. Factor x x – 48. Identify the pair of factors of –48 that has a sum of 13. b. Factor n 2 – 5n – 24. Identify the pair of factors of –24 that has a sum of –5. x x – 48 = (x + 16)(x – 3) n 2 – 5n – 24 = (n + 3)(n – 8) Factors of –48Sum of Factors 1 and –48–47 48 and – and –24–22 24 and – and –16–13 16 and –3 13 Factors of –24Sum of Factors 1 and –24–23 24 and– and–12–10 12 and– and–8 –5 How does the factors change when the last term is negative? What happens when the 2d and 3d terms are negative? Factoring a Quadratic Equation

Factor d dg – 60g 2. Factors of –60Sum of Factors 1 and –60–59 60 and – and –30–28 30 and – and –20–17 20 and –3 17 Find the factors of –60. Identify the pair that has a sum of 17. d dg – 60g 2 = (d – 3g)(d + 20g) What happens when there are 2 variables? Factor h 2 – 4hk – 77k 2. Factors of –77Sum of Factors 1 and –77–76 77 and – and –7 4 7 and – h 2 – 4hk – 77k 2 = (h + 7k)(h – 11k)