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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 ax2 + 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. BACK

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**Examples of Quadratic Equations**

Standard Form BACK

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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 BACK

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**Solve the equation. Check your answers.**

Solution Set OR BACK

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**Solve each equation. Check your answers.**

OR Solution Set BACK

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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. BACK

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Solve. BACK

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Solve. BACK

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Solve. BACK

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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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**Set each of the three factors equal to 0.**

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

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Solve. BACK

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**x2 – 9x + 20 = 0 (x – 4)(x – 5) = 0 x – 4 = 0 x = 4 x – 5 = 0 x = 5**

Example: Standard form already Factor Set each factor = 0 Solve Write the solution set BACK

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**4x2 – 49 = 0 (2x + 7)(2x – 7) = 0 2x + 7 = 0 2x – 7 = 0 Example**

Standard form already Factor Set each factor = 0 Solve Write the solution set BACK

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Solving Equations Now that we know how to factor, we can apply this knowledge to the solution of equations. How would you solve the following equation? x2 – 36 = 0 Step 1: Factor the polynomial. (x - 6)(x + 6) = 0

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Solving Equations Step 2: Apply the zero product property which states that For all numbers a and b, if ab = 0, then a = 0, b = 0, or both a and b equal 0. (x - 6)(x + 6) = 0 Therefore (x – 6) = 0 or (x + 6) = 0. x + 6 = 0 x – 6 = 0 or x = 6 x = -6 This equation has two solutions or zeros: x = 6 or x = -6.

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**x2 – 25 = 0 x2 + 7x – 8 = 0 x2 – 12x + 36 = 0 c2 – 8c = 0 You Try It**

Solve the following equations. x2 – 25 = 0 x2 + 7x – 8 = 0 x2 – 12x + 36 = 0 c2 – 8c = 0

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Summary of Steps Get a value of zero on one side of the equation. Factor the polynomial if possible. Apply the zero product property by setting each factor equal to zero. 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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