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1 5.12 Solving Quadratic Equations by Factoring Algebra I

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2 Zero-Factor Property Let a and b be real numbers, variables or algebraic expressions and factors such that a*b=0; THEN a = 0 or b= 0. This property also applies to three or more factors.

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3 Zero Factor property This property is the primary property for solving equations in algebra For example, to solve the equation (x-1)(x+2) = 0 you can use the zero factor property to conclude that either x-1=0 or x+2 = 0. If we set the first factor to 0, x = 1; if we set the second factor to 0, x = -2 So the equation (x-1)(x+2) =0 has exactly two solutions : 1 and -2. You can check your answers.

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4 Quadratic equation A quadratic equation is an equation that can be written in the general form ax 2 + bx + c = 0 where a, b and c are real numbers and a does not equal 0. You are going to combine your factoring skills with the Zero-Factor property to solve quadratic equations.

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5 Steps for solving quadratic equations 1. Write the quadratic equation in general form. 2. Factor the left side of the equation. 3. Set each factor with a variable equal to zero. 4. Solve each linear equation 5. Check each solution in the original equation

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6 Solving equations (s-4)(s-10) = 0 X 2 -144 = 0 6x 2 + 3x = 0 y(y-4) + 3(y-4)=0

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More Examples 1) 2) 3) 4) 5) 7

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8 Quadratic equation with a repeated solution If you have a perfect square trinomial, your factors are the same…so, you will only have one solution x 2 -8x + 16=0 Factor: (x-4)(x-4) Set x-4 = 0 x = 4

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9 Solving a quadratic equation by factoring Solve (x+1)(x-2) =4 Don’t make the mistake of setting x+1 equal to 4. You must first satisfy the zero property rule, so you need to do FOIL and then factor and set to zero! x 2 -x-2=4 so x 2 -x-6 = 0 (x-3)(x+2) = 0, so x = 3 and x = -2

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