7 5 Factoring Special Products Warm Up Lesson

7 -5 Factoring. Special. Products Warm Up Lesson Presentation Lesson Quiz Holt Mc. Dougal Algebra 1 Algebra 11 Holt Mc. Dougal

7 -5 Factoring Special Products Warm Up Determine whether the following are perfect squares. If so, find the square root. 1. 64 2. 36 yes; 6 3. 45 5. y 8 4. x 2 yes; x Holt Mc. Dougal Algebra 1

7 -5 Factoring Special Products ESSENTIAL QUESTION How do you factor perfect-square trinomials and the difference of two squares? Holt Mc. Dougal Algebra 1

7 -5 Factoring Special Products Holt Mc. Dougal Algebra 1

7 -5 Factoring Special Products Example 1 A: Recognizing and Factoring Perfect. Square Trinomials Determine whether each trinomial is a perfect square. If so, factor. If not explain. 9 x 2 – 15 x + 64 3 x 3 x 2(3 x 8) 8 8 2(3 x 8) ≠ – 15 x. 9 x 2 – 15 x + 64 is not a perfect-square trinomial because – 15 x ≠ 2(3 x 8). Holt Mc. Dougal Algebra 1

7 -5 Factoring Special Products Example Determine whether each trinomial is a perfect square. If so, factor. If not explain. Method 2 Use the rule. 81 x 2 + 90 x + 25 a = 9 x, b = 5 (9 x)2 + 2(9 x)(5) + 52 Write the trinomial as a 2 + 2 ab + b 2. (9 x + 5)2 Write the trinomial as (a + b)2. Holt Mc. Dougal Algebra 1

7 -5 Factoring Special Products Example: Recognizing as Perfect-Square Trinomials 36 x 2 – 10 x + 14 is not a perfect-square trinomial. Holt Mc. Dougal Algebra 1

7 -5 Factoring Special Products Example Determine whether each trinomial is a perfect square. If so, factor. If not explain. Method 1 Factor. x 2 + 4 x + 4 Factors of 4 Sum (1 and 4) 5 (2 and 2) 4 (x + 2) = (x + 2)2 Holt Mc. Dougal Algebra 1

7 -5 Factoring Special Products Example Determine whether each trinomial is a perfect square. If so, factor. If not explain. Method 2 Use the rule. x 2 – 14 x + 49 a = 1, b = 7 (x)2 – 2(x)(7) + 72 (x – 7)2 Holt Mc. Dougal Algebra 1 Write the trinomial as (a – b)2.

7 -5 Factoring Special Products Holt Mc. Dougal Algebra 1

7 -5 Factoring Special Products Example: Recognizing and Factoring the Difference of Two Squares 3 p 2 – 9 q 4 3 q 2 3 p 2 is not a perfect square. 3 p 2 – 9 q 4 is not the difference of two squares because 3 p 2 is not a perfect square. Holt Mc. Dougal Algebra 1

7 -5 Factoring Special Products Example Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 100 x 2 – 4 y 2 100 x 2 10 x – The polynomial is a difference of two squares. 4 y 2 2 y 2 y (10 x)2 – (2 y)2 (10 x + 2 y)(10 x – 2 y) Holt Mc. Dougal Algebra 1 a = 10 x, b = 2 y Write the polynomial as (a + b)(a – b).

7 -5 Factoring Special Products Example Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. x 4 – 25 y 6 x 2 5 y 3 (x 2 + 5 y 3)(x 2 – 5 y 3) Holt Mc. Dougal Algebra 1

7 -5 Factoring Special Products Example Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 1 – 4 x 2 1 1 2 x 2 x (1 + 2 x)(1 – 2 x) 1 – 4 x 2 = (1 + 2 x)(1 – 2 x) Holt Mc. Dougal Algebra 1

7 -5 Factoring Special Products Example Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. p 8 – 49 q 6 p 4 – p 4 7 q 3 – 7 q 3 (p 4 + 7 q 3)(p 4 – 7 q 3) Holt Mc. Dougal Algebra 1

7 -5 Factoring Special Products Example Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 16 x 2 – 4 y 5 4 x Holt Mc. Dougal Algebra 1 4 y 5 is not a perfect square.

7 -5 Factoring Special Products Lesson Quiz: Part I Determine whether each trinomial is a perfect square. If so factor. If not, explain. 1. 64 x 2 – 40 x + 25 2. 121 x 2 – 44 x + 4 3. 49 x 2 + 140 x + 100 Holt Mc. Dougal Algebra 1

7 -5 Factoring Special Products Lesson Quiz: Part II Determine whether the binomial is a difference of two squares. If so, factor. If not, explain. 5. 9 x 2 – y 4 6. 30 x 2 – y 2 7. x 2 – y 8 Holt Mc. Dougal Algebra 1