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Objective 14 – Null Factor Law and Solving Quadratic Equations: What is the null factor law? Given that : AB 0 Then either A 0 or B 0 Why is this important to know? We will use the null factor law to solve quadratic equations. Ex: Solve for x: x 2 x 72 0 In this problem it is hard to isolate x. However if we factor the left hand side of the equation we create a situation where we are multiplying two things together that equals zero: x 2 x 72 0 ( x 9)( x 8) 0 Now we will apply the null factor law: ( means therefore ) x 2 x 72 0 ( x 9)( x 8) 0 either ( x 9) 0 or ( x 8) 0 To finish the problem we must solve for x in each equation: x 2 x 72 0 ( x 9)( x 8) 0 either ( x 9) 0 or ( x 8) 0 x 9 or x 8 What do the answers x 9 and x 8 mean to the problem? x 9 and x 8 are the values of x that make the equation true let x 9 x 2 x 72 0 (9) 2 (9) 72 0 81 81 0 00 This is true let x 8 and x 2 x 72 0 (8) 2 (8) 72 0 72 72 0 00 This is true More Examples: a) x2 x 0 x( x 1) 0 either x 0 or x 1 0 x 0 or x 1 9x3 x 0 b) c) ( x)(9 x 2 1) 0 ( x)(3x 1)(3x 1) 0 either x 0 or 3x 1 0 or 3x 1 0 1 1 x 0 or x or x 3 3 x 2 12 x 11 0 ( x 11)( x 1) 0 either x 11 0 or x 1 0 x -11 or x 1 2x 2 x 6 0 2 x 2 4 x 3x 6 0 (2 x)( x 2) 3( x 2) 0 d) ( x 2)( 2 x 3) 0 either x 2 0 or 2 x 3 0 x -2 or x 3 2