1. Transparency 6 Click the mouse button or press the Space Bar to display the answers.

2. Example 6-1a Determine whether is a perfect square trinomial. If so, factor it. Answer:is a perfect square trinomial. 3. Is the middle term equal to? Yes, 1. Is the first term a perfect square? Yes, 2. Is the last term a perfect square?Yes, Write as Factor using the pattern.

3. Example 6-1a Determine whether is a perfect square trinomial. If so, factor it. 1. Is the first term a perfect square? Yes, 2. Is the last term a perfect square?Yes, 3. Is the middle term equal to? No, Answer:is not a perfect square trinomial.

4. Example 6-1b Determine whether each trinomial is a perfect square trinomial. If so, factor it. a. b. Answer: not a perfect square trinomial Answer: yes;

5. Example 6-2a Factor. First check for a GCF. Then, since the polynomial has two terms, check for the difference of squares. 6 is the GCF. and Factor the difference of squares. Answer:

6. Example 6-2a Factor. This polynomial has three terms that have a GCF of 1. While the first term is a perfect square, the last term is not. Therefore, this is not a perfect square trinomial. This trinomial is in the formAre there two numbers m and n whose product is and whose sum is 8 ? Yes, the product of 20 and –12 is –240 and their sum is 8.

7. Example 6-2a Write the pattern. and Group terms with common factors. Factor out the GCF from each grouping. is the common factor. Answer:

8. Example 6-2b Factor each polynomial. a. b. Answer:

9. Example 6-3a Solve Recognize as a perfect square trinomial. Original equation Factor the perfect square trinomial. Set the repeated factor equal to zero. Solve for x. Answer: Thus, the solution set isCheck this solution in the original equation.

10. Example 6-3b Solve Answer:

11. Example 6-4a Solve. Original equation Square Root Property Add 7 to each side. Simplify. Separate into two equations. or Answer: The solution set isCheck each solution in the original equation.

12. Example 6-4a Solve. Original equation Recognize perfect square trinomial. Factor perfect square trinomial. Square Root Property Subtract 6 from each side.

13. Example 6-4a Answer: The solution set isCheck this solution in the original equation. or Separate into two equations. Simplify.

14. Example 6-4a Solve. Original equation Square Root Property Subtract 9 from each side. Answer: Since 8 is not a perfect square, the solution set is Using a calculator, the approximate solutions areor about –6.17 and or about –11.83.

15. Example 6-4a Check You can check your answer using a graphing calculator. GraphandUsing the INTERSECT feature of your graphing calculator, find whereThe check of –6.17 as one of the approximate solutions is shown.

16. Solve each equation. Check your solutions. a. b c. Example 6-4b Answer: