Warm Up Determine whether the following are perfect squares. If so, find the square root. 64

1. Warm Up • Determine whether the following are perfect squares. If so, find the square root. • 64 yes; 6 2. 36 yes; 8 no 3. 45 4. x2 yes; x 5. y8 yes; y4 yes; 2x3 6. 4x6 no 7. 9y7 8. 49p10 yes;7p5

2. B. Find the degree of each polynomial. A. 11x7 + 3x3 D. x3y2 + x2y3 – x4 + 2 7 5 4 C. 5x – 6 1 The degree of a polynomial is the degree of the term with the greatest degree.

3. Objectives Factor perfect-square trinomials. Factor the difference of two squares.

4. 3x3x 2(3x2) 22 • • • 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 + 12x + 4

6. 3x3x 2(3x8) 88  2(3x 8) ≠ –15x.    9x2– 15x + 64 is not a perfect-square trinomial because –15x ≠ 2(3x  8). Determine whether each trinomial is a perfect square. If so, factor. If not explain. 9x2– 15x + 64

7. 9x9x 2(9x5) 55 ● ● ● Determine whether each trinomial is a perfect square. If so, factor. If not explain. 81x2 + 90x + 25 The trinomial is a perfect square. Factor. 81x2 + 90x + 25

8. Determine whether each trinomial is a perfect square. If so, factor. If not explain. 36x2– 10x + 14 The trinomial is not a perfect-square because 14 is not a perfect square.

9. x2 + 4x + 4 x x 2(x2) 22    Determine whether each trinomial is a perfect square. If so, factor. If not explain. The trinomial is a perfect square. Factor.

10. 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. 16x2– 24x + 9 16x2– 24x + 9

11. 4x2–9 2x 2x3 3   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.

12. 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.

13. 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.

14. 100x2– 4y2 10x 10x 2y 2y   Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. The polynomial is a difference of two squares. Write the polynomial as (a + b)(a – b). 100x2– 4y2 = (10x + 2y)(10x– 2y)

15. x2 x2 5y3 5y3   Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. x4– 25y6 The polynomial is a difference of two squares. Write the polynomial as (a + b)(a – b). x4– 25y6 = (x2 + 5y3)(x2– 5y3)

16. 1 1 2x 2x   Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 1 – 4x2 The polynomial is a difference of two squares. Write the polynomial as (a + b)(a – b). 1 – 4x2 = (1+ 2x)(1 – 2x)

17. p4 p4 7q3 7q3 ● ● Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. p8– 49q6 The polynomial is a difference of two squares. Write the polynomial as (a + b)(a – b). p8– 49q6 = (p4 + 7q3)(p4– 7q3)

18. 4x 4x 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 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