Warm-up: Factor 3x2 + 19x - 14 a = 3 b = 19 c = -14 Use the X-box: x 7 a·c 3x2 21x -42 3x X 21 -2 -2x -14 19 -2 b (3x – 2)(x + 7)

Agenda Warmup Check Homework Notes 7-4C Assignment

Lesson 7.4C Learning Target: More solving equations in the form ax2+bx+c = 0

18 X 9 2 11 (x + 3)(3x + 2) = 0 3x2 9x 2x 6 EX 1: 3x2 + 11x + 6 = 0 x No common factors! a = 3 b = 11 c = 6 Use the X-box: x 3 a·c 3x2 9x 18 3x X 9 2 2x 6 11 2 b (x + 3)(3x + 2) = 0

(x + 3)(3x +2) = 0 3x + 2 = 0 x + 3 = 0 x = -3 3x = -2 x = -2/3 Now, set each factor equal to zero and solve: 3x + 2 = 0 x + 3 = 0 -3 -3 -2 -2 x = -3 3x = -2 x = -2/3

EX 2: 4x2 + 19x – 5 = 0 No common factors! a = 4 b = 19 c = -5 Use the X-box: x 5 a·c 4x2 20x -20 4x X 20 -1 -1x -5 19 -1 b (x + 5)(4x – 1) = 0

(x + 5)(4x – 1) = 0 4x – 1 = 0 x + 5 = 0 x = -5 4x = 1 x = 1/4 Now, set each factor equal to zero and solve: 4x – 1 = 0 x + 5 = 0 -5 -5 + 1 +1 x = -5 4x = 1 x = 1/4

EX 3: 4x2 – 20x + 21 = 0 No common factors! a = 4 b = -20 c = 21 Use the X-box: 2x -7 a·c 4x2 -14x 84 2x X -6 -14 -6x 21 -20 -3 b (2x – 7)(2x – 3) = 0

(2x – 7)(2x – 3) = 0 2x – 3 = 0 2x – 7 = 0 2x = 7 2x = 3 x = 3/2 Now, set each factor equal to zero and solve: 2x – 3 = 0 2x – 7 = 0 + 3 +3 +7 +7 2x = 7 2x = 3 x = 3/2 x = 7/2

Are you a Master? Solve the following equations. #1: Solve 4x2 + 1x - 14 = 0 #2: Solve 12x2 + 10 = 23x x= -2, x = 7/4 or 1.75 x= 2/3, x = 5/4 or 1.25

Remember????? Solving polynomials with boxes EXAMPLE 4: Factor 4x + 8 Make a rectangle with two boxes, putting each term in its own box 2. Label the width with the GCF of the terms x 2 4 (x + 2)= 0 X + 2 = 0 4x 8 4 X = -2

Factoring polynomials with boxes Remember????? Factoring polynomials with boxes EXAMPLE 5: Factor x2 – 5x Make a rectangle using these terms x - 5 x (x - 5) x2 -5x x X = 0 x – 5 = 0 x = 5

What is the difference between FACTOR and SOLVE????? So wait????? What is the difference between FACTOR and SOLVE?????

Assignment 7-4C: