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Solving Equations by Factoring Definition of Quadratic Equations Zero-Factor Property Strategy for Solving Quadratics

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Standard Form Quadratic Equation Quadratic equations can be written in the form ax 2 + bx + c = 0 where a, b, and c are real numbers with a 0. Standard form for a quadratic equation is in descending order equal to zero.

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Examples of Quadratic Equations Standard Form

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Zero-Factor Property If a and b are real numbers and if ab =0, then a = 0 or b = 0. BACK

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Solve the equation (x + 2)(2x - 1)=0 By the zero factor property we know... Since the product is equal to zero then one of the factors must be zero. OR

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Solve the equation. Check your answers. OR Solution Set

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Solve each equation. Check your answers. OR Solution Set

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Solving a Quadratic Equation by Factoring Step 1 Write the equation in standard form. Step 2 Factor completely. Step 3 Use the zero-factor property. Set each factor with a variable equal to zero. Step 4 Solve each equation produced in step 3.

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Solve.

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Number Of Solutions The degree of a polynomial is equal to the number of solutions. Three solutions!!!

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x (x + 1)(x – 3) = 0 Set each of the three factors equal to 0. x = 0 x + 1 = 0 x = -1 x – 3 = 0 x = 3 Solve the resulting equations. Write the solution set. x = {0, -1, 3}

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Solve.

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x 2 – 9x + 20 = 0 (x – 4)(x – 5) = 0 x – 4 = 0 x = 4 x – 5 = 0 x = 5 x = {5, 4} Standard form already Factor Set each factor = 0 Solve Write the solution set

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Example 4x 2 – 49 = 0 (2x + 7)(2x – 7) = 0 2x + 7 = 0 2x – 7 = 0 Standard form already Factor Set each factor = 0 Solve Write the solution set

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This equation has two solutions or zeros: x = 6 or x = -6. How would you solve the following equation? x2 x2 – 36 = 0 Factor the polynomial. (x - 6)(x + 6) = 0 Therefore (x – 6) = 0 or (x + 6) = 0. x – 6 = 0 + 6 +6 x = 6 or x + 6 = 0 - 6 -6 x = -6

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Solve the following equations. 1.x 2 – 25 = 0 2.x 2 + 7x – 8 = 0 3.x 2 – 12x + 36 = 0 4.c 2 – 8c = 0

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1.Get a value of zero on one side of the equation. 2.Factor the polynomial if possible. 3.Apply the zero product property by setting each factor equal to zero. 4.Solve for the variable.

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Solving Equations by Factoring Definition of Quadratic Equations Zero-Factor Property Strategy for Solving Quadratics

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