1. Section 4.4 – Factoring Quadratic Expressions Factors of a given number are numbers that have a product equal to the given numbers. Factors of a given expression are expressions that have a product equal to the given expression. Factoring is rewriting an expression as a product of its factors.

2. Section 4.4 – Factoring Quadratic Expressions Essential Understanding: You can use the Distributive Property or the FOIL method to multiply two binomials. (x + 4)(x+2) = _____________

3. Section 4.4 – Factoring Quadratic Expressions Essential Understanding: To factor x 2 + 6x + 8, think FOIL in reverse. Find two binomials for which the first terms have the product of x 2, the products of the outer and the inner have the sum of 6x, and the last terms have the product of 8. x 2 + 6x + 8 = ___________________

4. Section 4.4 – Factoring Quadratic Expressions Problem 1: What is the expression in factored form? x 2 + 9x + 20

5. Section 4.4 – Factoring Quadratic Expressions Problem 1: What is the expression in factored form? x 2 + 14x – 72

6. Section 4.4 – Factoring Quadratic Expressions Problem 1: What is the expression in factored form? -x 2 + 13x – 12

7. Section 4.4 – Factoring Quadratic Expressions Problem 1: What is the expression in factored form? x 2 – 11x + 30

8. Section 4.4 – Factoring Quadratic Expressions Problem 1: What is the expression in factored form? -x 2 + 14x + 32

9. Section 4.4 – Factoring Quadratic Expressions The greatest common factor (GCF) of an expression is a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent.

10. Section 4.4 – Factoring Quadratic Expressions Problem 2: What is the expression in factored form? 6n 2 + 9n

11. Section 4.4 – Factoring Quadratic Expressions Problem 2: What is the expression in factored form? 4x 2 + 20x – 56

12. Section 4.4 – Factoring Quadratic Expressions Problem 2: What is the expression in factored form? 7m 2 – 21

13. Section 4.4 – Factoring Quadratic Expressions Problem 2: What is the expression in factored form? 9x 2 + 9x – 18

14. Section 4.4 – Factoring Quadratic Expressions Problem 2: What is the expression in factored form? 4x 2 + 8x + 12

15. Section 4.4 – Factoring Quadratic Expressions Problem 3: What is the expression in factored form? 2x 2 + 11x + 12

16. Section 4.4 – Factoring Quadratic Expressions Problem 3: What is the expression in factored form? 4x 2 – 4x – 3

17. Section 4.4 – Factoring Quadratic Expressions Problem 3: What is the expression in factored form? 4x 2 +7x + 3

18. Section 4.4 – Factoring Quadratic Expressions Problem 3: What is the expression in factored form? 2x 2 – 7x + 6

19. Section 4.4 – Factoring Quadratic Expressions Problem 3: What is the expression in factored form? 2x 2 +2x + 2

20. Section 4.4 – Factoring Quadratic Expressions A perfect square trinomial is a trinomial that is the square of a binomial. For example, x 2 + 10x + 25 = (x+5) 2

21. Section 4.4 – Factoring Quadratic Expressions If ax 2 +bx +c is a perfect square trinomial, then ax 2 and c are squares of the terms of the binomial and thus are both positive. bx is twice the product of the terms of the binomial.

22. Section 4.4 – Factoring Quadratic Expressions

23. Problem 4: What is x 2 – 6x + 9 in factored form

24. Section 4.4 – Factoring Quadratic Expressions Problem 4: What is 64x 2 +16x + 1 in factored form

25. Section 4.4 – Factoring Quadratic Expressions Problem 4: What is 4x 2 – 20x + 25 in factored form

26. Section 4.4 – Factoring Quadratic Expressions The expression a 2 – b 2 is the difference of two squares. There is a pattern to its factors.

27. Section 4.4 – Factoring Quadratic Expressions Problem 5: What is 25x 2 – 49 in factored form?

28. Section 4.4 – Factoring Quadratic Expressions Problem 5: What is 16x 2 – 81 in factored form?

29. Section 4.4 – Factoring Quadratic Expressions Problem 5: What is 81x 2 + 49 in factored form?