Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig Aim: How to solve quadratic equations? Do Now: I III II Rectangular Box Rectangular Prism In the figure above, for all values of x > 1, the area of face I is x 2 - 1, and the area of face II is x 2 + 3x + 2. Which of the following represents the area of face III? A) x 2 + 3x + 1 B) x 2 - 3x + 2 C) 2x 2 + 3x + 1 D) x 2 + x - 2 E) x 2 - 2x - 2

Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig Quadratic Equations x 2 + 4x + 3 = y What if x 2 + 4x + 3 = 0, What value of x would make this a true statement? x 2 + 4x + 3= (x + 3)(x + 1)= 0 Zero Product Property (x + 3)(x + 1) = 0 (x + 3) = 0 x = -3 (x + 1) = 0 x = -1 Substitute and Check = (x + 3)(x + 1)

Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig Zero Product Property Any term multiplied by zero equals zero. Zero Product Property 4 · 0 = 0 xy = 0 x · 0 = 0 Either x or y or both are equal to zero x 2 + 4x + 3= (x + 3)(x + 1)= 0

Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig ax 2 + bx + c = 0 a, b, and c are real numbers; a = 0 Example: 2x 2 + 9x + 10 = 0 Polynomial with one variable. Second degree equation -greatest exponent is two ( 2 ). Standard form: Descending order of exponents left to right. All terms collected to one side and the entire polynomial is equal to zero (0). Solving Quadratic Equations

Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig x x + 50 = 0 Put in Standard from if not already x x + 50 = 0 Factor: (x + 5)(x + 10) = 0 Set each factor equal to 0 x + 5 = 0x + 10 = 0 x = -5x = -10 Substitute and Check (-5) (-5) = = -50 T (-10) (-10) = (-150) = -50T For this to be true one factor must equal zero. Quadratic Equations: Factoring Trinomial

Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig x 2 = 25 Put in Standard from if not already x = 0 Factor: (x - 5)(x + 5) = 0 Set each factor equal to 0 x - 5 = 0x + 5 = 0 x = 5x = -5 Substitute and Check 5 2 = 25T (-5) 2 = 25T Note Quadratic Equations: Diff. of Squares

Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig 12x 2 = 24x Put in Standard from if not already 12x x = 0 Factor: 6x(2x - 4) = 0 Substitute and Check 12(0) 2 = 24(0) 0 = 0 T 12(2) 2 = 24(2) 48 = 48T Set each factor equal to 0 6x = 02x - 4 = 0 x = 02x = 4x = 2 Quadratic Equations: GCF

Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig Model Problem Solve: 4x 2 – 14 = 2x 2 4x 2 – 2x 2 – 14 = 0 2x 2 – 14 = 0 2(x 2 – 7) = 0 ? 2x 2 = 14 x 2 = 7

Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig Model Problem Solve: y 2 – 7y + 6 = 0

Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig Model Problem Solve: x 2 – 25 = 25

Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig Model Problem Solve: x 2 – 4 = 80 – 2x 2

Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig Quadratic Verbal Problems The square of a number decreased by 4 times the number equals 21. Find the number. Let n equal the number The square of the number - n 2 Four times a number - 4n n 2 - 4n = Put in standard form n 2 - 4n - 21 = 0 2. Factor (n - 7)(n + 3) = 0 3. Set each factor equal to zero and solve. n + 3 = 0n = -3 n - 7 = 0n = 7

Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig Quadratic Verbal Problems The product of two consecutive, positive, even integers is 80. Find the integers. n - first of the consecutive, positive, even integers n + 2 the next consecutive, positive, even integer n(n + 2) 1. Put in standard form n 2 + 2n = 80 n 2 + 2n - 80 = 0 2. Factor (n + 10)(n - 8) = 0 3. Set each factor equal to zero and solve. n - 8 = 0 n = 8 n + 10 = 0 n = = 80

Aim: Solving Quadratic Equation by Factoring Course: Adv. Alg. & Trig Quadratic Verbal Problems The base of a parallelogram measures 7 centimeters more than its altitude. If the area of the parallelogram is 30 square centimeters, find the measure of its base and the measure of its altitude. x x = altitude (height) x + 7 x + 7 = base Area of parallelogram A = bh x(x + 7) = 30 x 2 + 7x = 30 x 2 + 7x - 30 = 0 x + 10 = 0 x = -10 x - 3 = 0 x = 3 x + 7 = 10ht. base Area = 30 (x + 10)(x - 3) = 0