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

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.

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.

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;

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:

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.

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

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

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.

Example 6-3b Solve Answer:

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.

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

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

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.

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.

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