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Solving Quadratic Equations …by Factoring. Solving Quadratic Equations by Factoring Get ZERO on one side by itself. Factor. Consider Common Factors FIRST!

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Presentation on theme: "Solving Quadratic Equations …by Factoring. Solving Quadratic Equations by Factoring Get ZERO on one side by itself. Factor. Consider Common Factors FIRST!"— Presentation transcript:

1 Solving Quadratic Equations …by Factoring

2 Solving Quadratic Equations by Factoring Get ZERO on one side by itself. Factor. Consider Common Factors FIRST! Set each factor = 0. Solve each part.

3 Example 3-1a Solveby factoring. Answer: The solution set is {0, –4}. Original equation Add 4x to each side. Factor the binomial. Solve the second equation. Zero Product Property or

4 Example 3-1a Check Substitute 0 and –4 in for x in the original equation.

5 Example 3-1a Solveby factoring. Original equation Subtract 5x and 2 from each side. Factor the trinomial. Zero Product Property or Solve each equation. Answer: The solution set is Check each solution.

6 Solve each equation by factoring. a. b. Example 3-1b Answer: {0, 3} Answer:

7 Example 3-2a Answer: The solution set is {3}. Solveby factoring. Original equation Add 9 to each side. Factor. Zero Product Property or Solve each equation.

8 Example 3-2a Check The graph of the related function, intersects the x -axis only once. Since the zero of the function is 3, the solution of the related equation is 3.

9 Example 3-2b Answer: {–5} Solveby factoring.

10 Example 3-3a Multiple-Choice Test Item What is the positive solution of the equation ? A –3 B 5 C 6 D 7 Read the Test Item You are asked to find the positive solution of the given quadratic equation. This implies that the equation also has a solution that is not positive. Since a quadratic equation can either have one, two, or no solutions, we should expect this equation to have two solutions.

11 Example 3-3a Solve the Test Item Answer: D Both solutions, –3 and 7, are listed among the answer choices. However, the question asks for the positive solution, 7. Original equation Factor. Divide each side by 2. Factor. or Zero Product Property Solve each equation.

12 Example 3-3b Multiple-Choice Test Item What is the positive solution of the equation ? A 5 B – 5 C 2 D 6 Answer: C

13 Example 3-4a Write a quadratic equation with and 6 as its roots. Write the equation in the form where a, b, and c are integers. Write the pattern. Simplify. Replace p with and q with 6.

14 Example 3-4a Use FOIL. Multiply each side by 3 so that b is an integer. Answer: A quadratic equation with roots and 6 and integral coefficients is You can check this result by graphing the related function.

15 Example 3-4b Write a quadratic equation with and 5 as its roots. Write the equation in the form where a, b, and c are integers. Answer:


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