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8-5 Factoring Special Products Warm Up Determine whether the following are perfect squares. If so, find the square root. 1. 64 3. 45 5. y8 7. 9y7 Holt Algebra 1 yes; 8 no yes; y4 no 2. 36 yes; 6 4. x2 yes; x yes; 2x3 6. 4x6 8. 49p10 yes;7p5 8-5 Factoring Special Products Find the degree of each polynomial. A. 11x7 + 3x3 7 D. x3y2 + x2y3 – x4 + 2 5 B. 4 C. 5x – 6 1 The degree of a polynomial is the degree of the term with the greatest degree. Holt Algebra 1 8-5 Factoring Special Products Learning Targets Students will be able to: Factor perfectsquare trinomials and factor the difference of two squares. Holt Algebra 1 8-5 Factoring Special Products A trinomial is a perfect square if: • The first and last terms are perfect squares. • The middle term is two times one factor from the first term and one factor from the last term. 9x2 3x Holt Algebra 1 • + 12x + 4 3x 2(3x • 2) 2 • 2 8-5 Factoring Special Products Holt Algebra 1 8-5 Factoring Special Products Determine whether each trinomial is a perfect square. If so, factor. If not explain. 9x2 – 15x + 64 3x 3x 2(3x 8) 8 8 2(3x 8) ≠ –15x. 9x2 – 15x + 64 is not a perfect-square trinomial because –15x ≠ 2(3x 8). Holt Algebra 1 8-5 Factoring Special Products Determine whether each trinomial is a perfect square. If so, factor. If not explain. 81x2 + 90x + 25 9x ● 9x 2(9x 81x2 + 90x + 25 Holt Algebra 1 ● 5) 5 ● 5 9 x 5 The trinomial is a perfect square. Factor. 2 8-5 Factoring Special Products Determine whether each trinomial is a perfect square. If so, factor. If not explain. 36x2 – 10x + 14 6x 6x ??? The trinomial is not a perfect-square because 14 is not a perfect square. Holt Algebra 1 8-5 Factoring Special Products Determine whether each trinomial is a perfect square. If so, factor. If not explain. x2 + 4x + 4 x x 2(x 2) 2 2 The trinomial is a perfect square. Factor. x 4x 4 x 2 2 Holt Algebra 1 2 8-5 Factoring Special Products A rectangular piece of cloth must be cut to make a tablecloth. The area needed is (16x2 – 24x + 9) in2. The dimensions of the cloth are of the form cx – d, where c and d are whole numbers. Find an expression for the perimeter of the cloth. Find the perimeter when x = 11 inches. 4x 3 16x2 – 24x + 9 4 x 4 x 2 4 x 3 16x2 – 24x + 9 4 x 3 P x 4 4x 3 Holt Algebra 1 33 2 4x 3 4x 3 P 11 4 4 11 3 164" 4x 3 8-5 Factoring Special Products In Chapter 7 you learned that the difference of two squares has the form a2 – b2. The difference of two squares can be written as the product (a + b)(a – b). You can use this pattern to factor some polynomials. A polynomial is a difference of two squares if: •There are two terms, one subtracted from the other. • Both terms are perfect squares. 4x2 – 9 2x Holt Algebra 1 2x 3 3 8-5 Factoring Special Products Reading Math Recognize a difference of two squares: the coefficients of variable terms are perfect squares, powers on variable terms are even, and constants are perfect squares. Holt Algebra 1 8-5 Factoring Special Products Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 3p2 – 9q4 ??? 3p2 is not a perfect square. 3p2 – 9q4 is not the difference of two squares because 3p2 is not a perfect square. Holt Algebra 1 8-5 Factoring Special Products Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 100x2 – 4y2 10x 10x 2y 2y The polynomial is a difference of two squares. Write the polynomial as (a + b)(a – b). 100x2 – 4y2 = (10x + 2y)(10x – 2y) Holt Algebra 1 8-5 Factoring Special Products Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. x4 – 25y6 x2 x2 5y3 5y3 The polynomial is a difference of two squares. Write the polynomial as (a + b)(a – b). x4 – 25y6 = (x2 + 5y3)(x2 – 5y3) Holt Algebra 1 8-5 Factoring Special Products Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 1 – 4x2 1 1 2x The polynomial is a difference of two squares. 2x Write the polynomial as (a + b)(a – b). 1 – 4x2 = (1 + 2x)(1 – 2x) Holt Algebra 1 8-5 Factoring Special Products Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. p8 – 49q6 p4 ● p4 7q3 ● 7q3 The polynomial is a difference of two squares. Write the polynomial as (a + b)(a – b). p8 – 49q6 = (p4 + 7q3)(p4 – 7q3) Holt Algebra 1 8-5 Factoring Special Products Check It Out! Example 3c Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 16x2 – 4y5 16x2 – 4y5 4x 4x 4y5 is not a perfect square. 16x2 – 4y5 is not the difference of two squares because 4y5 is not a perfect square. HW pp. 562-564/13-29 odd,46-50,55-64 Holt Algebra 1