5 Minute Check on Chapter 2 Transparency 3

5 -Minute Check on Chapter 2 Transparency 3 -1 1. Evaluate 42 - |x - 7| if x = -3 2. Find 4. 1 (-0. 5) Simplify each expression 3. 8(-2 c + 5) + 9 c 4. (36 d – 18) / (-9) 5. A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green? 6. Standardized Test Practice: A 8/4 < 4/8 B Which of the following is a true statement -4/8 < -8/4 C -4/8 > -8/4 Click the mouse button or press the Space Bar to display the answers. D -4/8 > 4/8

Lesson 9 -6 Perfect Squares and Factoring

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

Objectives • Factor perfect square trinomials • Solve equations involving perfect squares

Vocabulary • Perfect square- a number whose square root is a rational number • trinomial– the sum of three monomials

Factoring Perfect Square Trinomials • If a trinomial can be written in the form: a 2 + 2 ab + b 2 or a 2 – 2 ab + b 2 then it can be factored as (a + b)2 or as (a – b)2 respectively • Symbols: a 2 + 2 ab + b 2 = (a + b)2 or a 2 – 2 ab + b 2 = (a – b)2 • Examples: x 2 + 6 x + 9 = (x + 3)2 4 x 2 – 24 x + 36 = (2 x – 6)2

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

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

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

Example 2 b 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 form Are 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 2 b cont Write the pattern and Group terms with common factors Factor out the GCF from each grouping Answer: is the common factor.

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

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

Example 4 b Solve . Original equation Recognize perfect square trinomial Factor perfect square trinomial Square Root Property Subtract 6 from each side. or Separate into two equations. Simplify. Answer: The solution set is

Example 4 c 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 are or about – 6. 17 and or about – 11. 83.

Example 4 c cont Check You can check your answer using a graphing calculator. Graph and Using the INTERSECT feature of your graphing calculator, find where The check of – 6. 17 as one of the approximate solutions is shown.

Factoring Techniques • Greatest Common Factor (GCF) • Factor out a Common Factor • Difference of Squares • Perfect Square Trinomials • Factoring by Grouping

Summary & Homework • Summary: – If a trinomial can be written in the form a 2 + 2 ab + b 2 or a 2 – 2 ab + b 2, then it can be factored as (a + b)2 or (a – b)2, respectively – For a trinomial to be factorable as a perfect square, the first term must be a perfect square, the middle must be twice the product of the square roots of the first and last terms, and the last term must be a perfect square – Square Root Property: for any number n>0, if x 2 = n, then x = +- √n • Homework: – Pg. 512 18 -22, 26 -38, 44, 46