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

2. Find the degree of each polynomial.
A. 11x7 + 3x3
D. x3y2 + x2y3 – x4 + 2 7 5 B. 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. 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.
9x x
3x 3x
2(3x 2)
2 2 •

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

7. The trinomial is a perfect square. Factor.
Determine whether each trinomial is a perfect square. If so, factor. If not explain.
81x2 + 90x + 25
5 5
9x 9x
2(9x 5) ●
The trinomial is a perfect square. Factor.
81x2 + 90x + 25

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

10. A rectangular piece of cloth must be cut to make a tablecloth
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. A polynomial is a difference of two squares if:
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 2x 

12. 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.
Reading Math

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

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

16. Determine whether each binomial is a difference of two squares
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.
2x 2x 
Write the polynomial as (a + b)(a – b).
1 – 4x2 = (1 + 2x)(1 – 2x)

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

18. 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.  /13-29 odd,46-50,55-64