1. Section 4.3 Notes: Solving Quadratic Equations by Factoring

2. Review: Factoring using the Greatest Common Factor (GCF)
Example 1: Factor 9y2 + 3y. Example 2: Factor 5a2 – 20a.

3. Factoring a difference of two squares
Pattern: Example:
a2 – b2 = (a + b)(a – b) x2 – 9 = (x + 3)(x – 3)

4. Example 3: Factor 4x2 – 25
Example 4: Factor y2 – 36

5. Example 5: Factor 3y2 – 108 Example 6: Factor 64x2 – 121y2

6. Factoring using the Product Sum Method
Example 7: Factor x2 – 2x – 15.
Example 8: Factor x2 + 14x + 48.

7. Example 9: Factor 4x2 – 40x + 84

8. Steps to Slide and Divide
If a ≠ 1: ax2 + bx + c
Example:
2x2 + 17x + 21
1) Multiply a and c. (slide a to c)
2) Rewrite in the form x2 + bx + (ac)
3) Factor using product sum
4) Divide the numbers by a
5) Reduce fractions
6) Bring the denominator in front of the x.

9. Example 10: Factor 3x2 + 5x – 2.

10. Example 11: Factor 10x2 + 68x + 48.

11. Example 12: Factor 7x2 – 32x – 60.

12. Solving Quadratic Equations

13. Example 13: Solve (x + 2)x = 0

14. Example 14: Solve (x + 3)(x – 4) = 10

15. Example 15: Solve 5a2 – 20a = 0

16. Example 16: Solve x2 – 64 = 0

17. Example 17: Solve x2 + 14x = –48

18. Example 18: Find the zeros of 6x2 – 5x – 4 = 0

19. You can use the FOIL method to write a quadratic equation that is in factored form in standard form. The FOIL Method uses the Distributive Property to multiply binomials.

20. Example 19: Write a quadratic equation in standard form with and –5 as its roots.

21. Example 20: Write a quadratic equation with and 5 as its
roots. Write the equation in the form ax2 + bx + c = 0, where
a, b, and c are integers.

22. Example 21: The entrance to an office building is an arch in the shape of a parabola whose vertex is the height of the arch. The height of the arch is given by h = 9 – x 2, where x is the horizontal distance from the center of the arch. Both h and x are measured in feet. How wide is the arch at ground level?

23. Example 22: During a match, Andre hit a lob right off the court with the ball traveling in the shape of a parabola whose vertex was the height of the shot. The height of the shot is given by
h = 49 – x 2, where x is the horizontal distance from the center of the shot. Both h and x are measured in feet. How far was the lob hit?

24. Example 23: Find the value of x and the dimensions of the rectangle.

25. Example 24: Find the value of x and the dimensions of the rectangle.