Transparency 5 Click the mouse button or press the Space Bar to display the answers.

Example 5-1a Factor. Write in form Answer: Factor the difference of squares.

Example 5-1a Factor. Answer: Factor the difference of squares. and

Factor each binomial. a. b. Example 5-1b Answer:

Example 5-2a Factor The GCF ofand 27b is 3b. and Answer: Factor the difference of squares.

Example 5-2b Answer: Factor

Example 5-3a Factor The GCF of and 2500 is 4. and Factor the difference of squares. and Factor the difference of squares. Answer:

Example 5-3b Factor Answer:

Example 5-4a is the common factor. Factor the difference of squares, into. Answer: Factor Original Polynomial Factor out the GCF. Group terms with common factors. Factor each grouping.

Example 5-4b Factor Answer:

Example 5-5a Solveby factoring. Check your solutions. Original equation. and Factor the difference of squares. or Zero Product Property Solve each equation.

Example 5-5a Answer: The solution set is Check each solution in the original equation.

Example 5-5a Solveby factoring. Check your solutions. Original equation Subtract 3y from each side. The GCF of and 3y is 3y. and

Example 5-5a Answer: The solution set is Check each solution in the original equation. Applying the Zero Product Property, set each factor equal to zero and solve the resulting three equations. or

Answer: Solve each equation by factoring. Check your solutions. a. b. Example 5-5b Answer:

Example 5-6a Extended-Response Test Item A square with side length x is cut from a right triangle shown below. a. Write an equation in terms of x that represents the area A of the figure after the corner is removed. b.What value of x will result in a figure that is the area of the original triangle? Show how you arrived at your answer.

b. Find x so that A is the area of the original triangle, Example 5-6a Read the Test Item A is the area of the triangle minus the area of the square that is to be removed. Solve the Test Item a. The area of the triangle is or 64 square units and the area of the square is square units. Translate the verbal statement. Answer:

Example 5-6a Subtract 48 from each side. and Simplify. Factor the difference of squares. Simplify. or Zero Product Property Answer: Since length cannot be negative, the only reasonable solution is 4. Solve each equation.

a.Write an equation in terms of x that represents the area A of the figure after the corner is removed. b.What value of x will result in a figure that is of the area of the original square? Example 5-6b Extended-Response Test Item A square with side length x is cut from the larger square shown below. Answer: Answer: 3