Name
Class
Date
Practice
Perfect Squares and Factoring
Perfect Square Trinomial
a trinomial of the form
Squaring a Binomial
(a +
4)2 = a2 +
=
a2
+ 2ab +
b2
or
a2
- 2ab +
b2
a2
2(a)(4) +
+ 8a + 16
42
(2x - 3)2 = (2x )2 -2(2x )(3) + 32
=
4x 2
- 12x + 9
Factoring a Perfect Square Trinomial
a 2 + 8a + 16 = a2 + 2(a)(4) + 42
= (a + 4)2
4x 2 - 12x + 9 = (2x)2 -2(2x)(3) + 32
= (2x - 3)2
Determine whether each trinomial is a perfect square trinomial. If so, factor it.
1. x2 - 16x + 64
2. m2 + 10m + 25
3. p2 + 8p + 64
Factor each polynomial if possible. If the polynomial cannot be factored, write prime.
4. 98x2 - 200y2
5. x2 + 22x + 121
6. 81 + 18s + s2
7. 25c2 - 10c – 1
8. 169 - 26r + r2
10. 16m2 + 48m + 36
11. 16 - 25a2
12. b2 - 16b + 256
13. 36x2 - 12x + 1
14. 16a2 - 40ab + 25b2
15. 8m3 - 64m
9. 7x2 - 9x + 2
16.
PICTURE FRAMING Mikaela placed a frame around a
print that measures 10 inches by 10 inches. The area
of just the frame itself is 69 square inches.
What is the width of the frame?
Maintain Your Skills
1.
There are 32 founding members of an organization. The function y = 3x2 + 32 can be used to
determine the number of members in the organization after x months. Based on this function,
which statement is true?
A
The number of members in the organization increases by 9 members each month.
B
At the end of 16 months, there will be 288 members in the organization.
C
The number of members in the organization increases by 3 members each month.
D
At the end of 6 months, there will be 140 members in the organization.
2. The scatterplot below shows the relationship between the number of baseballs used in 14 games
and the number of pitches thrown in these games. Based on the scatterplot, what is the best
prediction of the number of baseballs that will be used if 275 pitches are thrown?
A
150
B
60
C
100
D
160
ANSWERS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
yes, (x – 8) (x – 8)
yes, (m + 5) (m + 5)
no
2(7x + 10y) (7x - 10y)
(x + 11)2
(9 + s)2
prime
(13 - r )2
(7x - 2) (x - 1)
4(2m + 3)2
(4 + 5a) (4 - 5a)
prime
(6x - 1)2
(4a - 5b)2
8m (m2 - 8)
1.5 in.
Maintain Your Skills
1.
2.
D
C