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Quadratic Equations Factoring Strategies

Learn how to factor quadratic equations by finding the greatest common factor, grouping terms, and using factoring rules. Practice with exercises and flow charts.

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Quadratic Equations Factoring Strategies

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  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

  10. Chapter 5 Factoring Section 5.1Exercise #5

  11. 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

  12. Section 5.2 Quadratic Equations

  13. Factor trinomials of the form A OBJECTIVES

  14. RULE Factoring Rule 1

  15. 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.

  16. 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.

  17. 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.

  18. Chapter 5 Factoring Section 5.2Exercise #6

  19. 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

  20. Section 5.3 Quadratic Equations

  21. Use the ac test to determine whether A OBJECTIVES

  22. B OBJECTIVES

  23. C OBJECTIVES

  24. 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.

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

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

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

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

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

  30. Chapter 5 Factoring Section 5.3Exercise #8

  31. 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

  32. 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

  33. Section 5.4 Quadratic Equations

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

  35. Factor a perfect square trinomial. B OBJECTIVES

  36. Factor the difference of two squares. C OBJECTIVES

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

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

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

  40. Chapter 5 Factoring Section 5.4Exercise #11

  41. 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

  42. Chapter 5 Factoring Section 5.4Exercise #13

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