1. Section 3.4 Homework Questions?

2. Section Concepts 3.4 Factoring Trinomials: Trial-and- Error Method Slide 2 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Factoring Trinomials by the Trial-and-Error Method

3. Section 3.4 Factoring Trinomials: Trial-and- Error Method 1.Factoring Trinomials by the Trial-and-Error Method Slide 3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The method presented in this section is called the trial-and- error method. We will factor quadratic trinomials of the form

4. Section We need to fill in the blanks so that the product of the first terms in the binomials is 2x 2 3.4 Factoring Trinomials: Trial-and- Error Method 1.Factoring Trinomials by the Trial-and-Error Method Slide 4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. and the product of the last terms in the binomials is 6. Furthermore, the factors of 2x 2 and 6 must be chosen so that the sum of the products of the inner terms and outer terms equals 7x.

5. PROCEDURETrial-and-Error Method to Factor ax 2 + bx + c (continued) Slide 5 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Step 1 Factor out the GCF. Step 2 List all pairs of factors of a and pairs of factors of c. Consider the reverse order for one of the lists of factors. Step 3 Construct two binomials of the form: Step 4 Test each combination of factors and signs until the sum of the products of the outer terms and inner terms gives the middle term. Step 5 If no combination of factors produces the correct product, the trinomial cannot be factored further and is a prime polynomial

6. PROCEDURESign Rules for the Trial-and-Error Method Slide 6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Given the trinomial ax 2 + bx + c, (a > 0), the signs can be determined as follows: If c is positive, then the signs in the binomials must be the same (either both positive or both negative). The correct choice is determined by the middle term. If the middle term is positive, then both signs must be positive. If the middle term is negative, then both signs must be negative.

7. PROCEDURESign Rules for the Trial-and-Error Method Slide 7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. If c is negative, then the signs in the binomial must be different. The middle term in the trinomial determines which factor gets the positive sign and which gets the negative sign.

8. Section 3.4 Factoring Trinomials: Trial-and- Error Method 1.Factoring Trinomials by the Trial-and-Error Method Slide 8 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Keep these two important guidelines in mind: For any factoring problem you encounter, always factor out the GCF from all terms first. To factor a trinomial, write the trinomial in the form ax 2 + bx + c. No binomial may contain a common factor

9. Example 1Factoring a Trinomial by the Trial- and-Error Method Slide 9 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the trial-and-error method:

10. Example 2Factoring a Trinomial by the Trial- and-Error Method Slide 10 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the trial-and-error method:

11. Example 3Factoring a Trinomial by the Trial- and-Error Method Slide 11 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the trial-and-error method:

12. Example 4Factoring a Trinomial by the Trial- and-Error Method Slide 12 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the trial-and-error method:

13. Example 5Factoring a Trinomial by the Trial- and-Error Method Slide 13 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the trial-and-error method:

14. Example 6Factoring a Trinomial by the Trial- and-Error Method Slide 14 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the trial-and-error method:

15. Example 7Factoring a Trinomial by the Trial- and-Error Method Slide 15 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the trial and error method:

16. Example 8Factoring a Trinomial by the Trial- and-Error Method Slide 16 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the trial-and-error method:

17. Example 9Factoring a Trinomial by the Trial- and-Error Method Slide 17 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the trial and error method:

18. Avoiding Mistakes Slide 18 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Do not forget to write the GCF in the final answer.

19. Section 3.4 Factoring Trinomials: Trial-and- Error Method You Try Slide 19 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the trial and error method

20. Section 3.4 Factoring Trinomials: Trial-and- Error Method You Try Slide 20 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the trial and error method

21. Section 3.4 Factoring Trinomials: Trial-and- Error Method You Try Slide 21 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Factor the trinomial by the trial and error method