Section 5.1

1. Section 5.1 Quadratic Equations

2. Find the greatest common factor (GCF) of numbers. Find the GCF of terms. A B OBJECTIVES

3. Factor out the GCF. Factor a four-term expression by grouping. C D OBJECTIVES

4. DEFINITION Greatest Common Factor (GCF) The largest common factor of the integers in a list.

5. PROCEDURE Finding the Product 4(x + y) = 4x + 4y 5(a – 2b) = 5a – 10b 2x(x + 3) = 2x2 + 6x

6. PROCEDURE Finding the Factors 4x + 4y = 4(x + y) 5a – 10b = 5(a – 2b) 2x2 + 6x = 2x(x + 3)

7. DEFINITION GCF of a Polynomial a is the greatest integer that divides each coefficient.

8. DEFINITION GCF of a Polynomial n is the smallest exponent of x in all the terms.

9. Chapter 5 Factoring Section 5.1Exercise #2

11. Chapter 5 Factoring Section 5.1Exercise #5

13. Factoring Strategy Flow Chart Factor out GCF (2) Terms (3) Terms (4) Terms • Difference of Squares • Sum/Difference of Cubes • Perfect Square Trinomial • (x2 + bx + c) • (ax2 + bx + c) • Grouping

15. Section 5.2 Quadratic Equations

16. Factor trinomials of the form A OBJECTIVES

17. RULE Factoring Rule 1

18. PROCEDURE Factoring x2 + bx + c Find two integers whose product is c and whose sum is b. If b and c are positive, both integers must be positive.

19. PROCEDURE Factoring x2 + bx + c Find two integers whose product is c and whose sum is b. If c is positive and b is negative, both integers must be negative.

20. PROCEDURE Factoring x2 + bx + c Find two integers whose product is c and whose sum is b. If c is negative, one integer must be negative and one positive.

21. Chapter 5 Factoring Section 5.2Exercise #6

23. Factoring Strategy Flow Chart Factor out GCF (2) Terms (3) Terms (4) Terms • Difference of Squares • Sum/Difference of Cubes • Perfect Square Trinomial • (x2 + bx + c) • (ax2 + bx + c) • Grouping

25. Section 5.3 Quadratic Equations

26. Use the ac test to determine whether A OBJECTIVES

27. B OBJECTIVES

28. C OBJECTIVES

29. TEST ac test for ax2 + bx + c A trinomial of the form ax2 + bx + c is factorable if there are two integers with product ac and sum b.

30. TEST ac test We need two numbers whose product is ac. The sum of the numbers must be b.

31. PROCEDURE Factoring by FOIL Product must be c. Product must be a.

32. PROCEDURE Factoring by FOIL The product of the numbers in the first (F) blanks must be a.

33. PROCEDURE Factoring by FOIL The coefficients of the outside (O) products and the inside (I) products must add up to b.

34. PROCEDURE Factoring by FOIL The product of numbers in the last (L) blanks must be c.

35. Chapter 5 Factoring Section 5.3Exercise #8

36. Factoring Strategy Flow Chart Factor out GCF (2) Terms (3) Terms (4) Terms • Difference of Squares • Sum/Difference of Cubes • Perfect Square Trinomial • (x2 + bx + c) • (ax2 + bx + c) • Grouping

38. Factoring Strategy Flow Chart Factor out GCF (2) Terms (3) Terms (4) Terms • Difference of Squares • Sum/Difference of Cubes • Perfect Square Trinomial • (x2 + bx + c) • (ax2 + bx + c) • Grouping

39. Section 5.4 Quadratic Equations

40. Recognize the square of a binomial (a perfect square trinomial). A OBJECTIVES

41. Factor a perfect square trinomial. B OBJECTIVES

42. Factor the difference of two squares. C OBJECTIVES

43. RULES Factoring Rules 2 and 3: PERFECT SQUARE TRINOMIALS

44. RULES Factoring Rules 2 and 3: PERFECT SQUARE TRINOMIALS

45. RULE Factoring Rule 4: THE DIFFERENCE OF TWO SQUARES

46. Chapter 5 Factoring Section 5.4Exercise #11

48. Factoring Strategy Flow Chart Factor out GCF (2) Terms (3) Terms (4) Terms • Difference of Squares • Sum/Difference of Cubes • Perfect Square Trinomial • (x2 + bx + c) • (ax2 + bx + c) • Grouping

50. Chapter 5 Factoring Section 5.4Exercise #13