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5.5 Solving Quadratic Equations by Factoring

5.5 Solving Quadratic Equations by Factoring. The form ax 2 + bx + c = 0 is the standard form of a quadratic equation. For example, and are all quadratic equations, but only x 2 + 5 x +6 = 0 is in standard form. Solving Quadratic Equations by Factoring. Quadratic Equation

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5.5 Solving Quadratic Equations by Factoring

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  1. 5.5 Solving Quadratic Equations by Factoring

  2. The form ax2 + bx + c = 0 is the standard form of a quadratic equation. For example, and are all quadratic equations, but only x2 + 5x +6 = 0 is in standard form. Solving Quadratic Equations by Factoring. Quadratic Equation A quadratic equation is an equation that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers, with a ≠ 0. Until now, we have factored expressions, including many quadratic expressions. In this section we see how we can use factored quadratic expressions to solve quadraticequations. Slide 5.5-3

  3. Objective 1 Solve quadratic equations by factoring. Slide 5.5-4

  4. Solve quadratic equations by factoring. We use the zero-factor property to solve a quadratic equation by factoring. Zero-Factor Property If a and b are real numbers and if ab = 0, then a = 0 or b = 0. That is, if the product of two numbers is 0, then at least one of the numbers must be 0. One number must, but both may be 0. Slide 5.5-5

  5. CLASSROOM EXAMPLE 1 Using the Zero-Factor Property Solution: Solve. or or Slide 5.5-6

  6. CLASSROOM EXAMPLE 2 Solving Quadratic Equations Solution: Solve each equation. or or Slide 5.5-7

  7. Solve quadratic equations by factoring. (cont’d) Solving a Quadratic Equation by Factoring Step 1:Write the equation in standard form —that is, with all terms on one side of the equals sign in descending power of the variable and 0 on the other side. Step 2:Factorcompletely. Step 3:Use the zero-factor propertyto set each factor with variable equal to 0, and solve the resulting equations. Step 4:Checkeach solution in the original equation. Slide 5.5-8

  8. A common error is to include the common factor 3 as a solution. Only factors containing variables lead to solutions. CLASSROOM EXAMPLE 3 Solving a Quadratic Equation with a Common Factor Solution: Solve 3m2− 9m = 30. Slide 5.5-9

  9. CLASSROOM EXAMPLE 4 Solving Quadratic Equations Solve each equation. Solution: Slide 5.5-10

  10. CLASSROOM EXAMPLE 4 Solving Quadratic Equations (cont’d) Solve the equation. Solution: Slide 5.5-11

  11. There is no need to write the same number more than once in a solution set when a double solution occurs. CLASSROOM EXAMPLE 5 Solving Quadratic Equations with Double Solutions Solve. Solution: Slide 5.5-12

  12. Objective 2 Solve other equations by factoring. Slide 5.5-13

  13. CLASSROOM EXAMPLE 6 Solving Equations with More than Two Variable Factors Solve the equation. Solution: Slide 5.5-14

  14. CLASSROOM EXAMPLE 6 Solving Equations with More Than Two Variable Factors (cont’d) Solve the equation. Solution: Slide 5.5-15

  15. CLASSROOM EXAMPLE 7 Solving an Equation Requiring Multiplication before Factoring Solve. Solution: Slide 5.5-16

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